I suppose you inserted your figure first by creating a frame (Insert>Frame>Frame...) and then added a caption with menu Insert>Caption ... after clicking inside the frame.
The dialog which opens allows you to set many properties of the caption.
If the preview does not show something like Figure 1.1, click on the Options button.
The first item in this second dialog is Numbering figures per chapter (or equivalent in your locale). The drop-down menu allows control on the number of levels displayed (from none up to 10). For chapter numbers only, choose Level: 1.
Other options are rather for fancy text decoration and layout but you can experiment to your liking.
Click OK twice and you’re done.
EDIT (to answer @Joeynn’s questions in comments)
Chapter numbering in captions will work only if outline numbering is enabled. You enable it with Tools>Chapter numbering... and choosing a numbering style for the adequate Heading x paragraph style.
If there is no numbering, chapter number is “void” and this “void” is transferred into the caption which gives a correctly numbered caption “void”-then-sequential-figure-number.
With chapter numbering enabled, you get chpter-number/separator-/sequential-number. If your chapter one contains no figure, the first figure in chapter two is captioned 2.1 as expected.
END OF EDIT
COMMENTS ON YOUR SAMPLE FILE
The most important comment is you are not using LO as it should be: there is a mixture of old-fashioned typewriter usage with modern document processing features. It looks like you are discovering /learning LO while you have a deadline with a professional task.
LO is based on styles, the most important of which are paragraph styles. Their parameters (attributes) allow you to set all visual characteristics of the geometric area occupied by the paragraph: spacing above and under (must never be achieved with “carriage return” strokes), alignment with page break (again, not to be done with carriage returns because a simple text update will ruin your manual sync), first line indent (without the need for Tab character).
Let’s start with your text. It is styled Default Style; it should be Text Body. Default Style is the ancestor of all styles and should be used only to set globally shared attributes, usually only the font.
Open the style navigator with F11. Right click Text Body and chose Modify.... Go to Indents & Spacing tab. Set First line indent to 1 cm, Spacing above and below to 0.3 cm (you may prefer some non symmetric values, experiment) and maybe Line spacing to Single instead of your 120%. Go to Alignment tab and set Options to Justified (it is usually better to justify paragraphs extending on the full width of the page). Click OK.
In your “main text” paragraphs, you can now suppress the initial Tabs and manual spacing above/under. With the cursor inside the paragraph, double-click on Text Body and your paragraph is restyled. All modifications made on the style will be instantly transferred to all such styled paragraphs.
Your bulleted paragraphs should likewise be styled List 1 and you can set the attributes independently from the “main text” paragraphs styled Text Body.
Now to the paragraphs making the outline of your documents, aka. chapters, sections, …
They should receive some Heading x style which are all children of Heading style. Heading, though child of Default Style, plays the same role as Default Style for all “titling” styles and should not be used in a document. You’ll set there the default font for all titles, usually a sans serif font (like Arial, Liberation Sans, Helvetica, …) because titles are bigger and shorter than “main text”.
Once this is done, modify Heading 1 used for chapter titling. When entering tabs, push Standard button to restore all attributes to parent’s values (thus erasing your present settings which might prevent automatic updates). Go to Indents & Spacing. Set Spacing above to 0 and below to 1 cm. Go to Text Flow tab. Check Breaks Insert to cause a page break before this paragraph. Go to Font tab to set character size (and eventually bold). If you find it convenient, go to Font Effects tab and choose Effects>Capitals (or Small Capitals) to spare you the pain of typing your title uppercase. Click OK
Customise your Heading 2 and Heading 3 to your taste.
Back to your text where you typed “Chapter X” in one paragraph and the title in another one, both styled Heading 1. The net result is: you have chapter 1 titled “CHAPTER 1” with empty contents and chapter 2 titled “LITERATURE …”. That is, you are now one off from the expected chapter number! The same holds for your subsequent chapters. It is easy to correct it.
Open Tools>Outline Numbering..., tab Numbering. In level 1, with Heading 1, make sure Number is set to 1, 2, 3, .... Set Separator Before to "CHAPTER " (with a space after the word) and nothing in After.
While you’re at it, correct your buggy levels 2 and 3. Level 2 should be set at Heading 2, 1, 2, 3, ..., Show sublevels 2 and erase Separator Before and After. Level 3 similarly is set at Heading 3, 1, 2, 3, ..., Show sublevels 3 and nothing in Separator Before and After. The chapter/section/subsection number will be automatically provided by LO.
Click OK.
Review your chapter titles. Erase the “CHAPTER X” paragraphs and manual spacings. You see your chapter title preceded by “CHAPTER x” and a Tab character. If you want the chapter number on an independent line, click between the Tab and the first character of your title and type Shift+Enter.
Note: since you seem to have manually formatted your titles, fully select the chapter title (triple-click is a shortcut) and Format>Clear Direct Formatting or Ctrl+M to reset all attributes to style values.
Review your section titles (paragraphs numbered with x.y) and re-style them as Heading 2 (The 2 here means "two numbers precede the paragraph). Thanks to LO, the first number is equal to chapter number. Consequently, do not use Heading 3 in your chapter 2!
You are now ready to face your original question: automatic figure numbering.
Select a figure (just click it once). Insert>Caption.... Type your caption in box Caption, without “Figure …”. Select Category as Figure (each category has its own numbering sequence). Click Options... to customise numbering and select how many “outline” numbers you want in the figure number: 1 for chapter only, 2 for chapter-section, 3 for chapter-section-subsection, etc. The choice you make here is global, i.e. you cannot have different number of levels in different parts of your document.
Figure numbers are entered into an LO dictionary and are available as automatically available references. In your text, instead of typing “see figure 2.1” which incurs the risk of being erroneous if you add a figure before this one, type "see figure " and Insert>Cross-reference.... In Type pane, select Figure, in Insert reference to choose Chapter for figure number and/or Reference for full title and click on the desired figure description. Click OK. If the figure number/title ever changes, the reference is magically updated.
I noticed you created your bibliography as a chapter. This is wrong. Conceptually, a bibliography is not a chapter, it is a table. Moreover, chapters have a number and bibliography none. With LO, you can’t have simultaneously numbered and unnumbered chapters. The solution to this dilemma is to use Insert>Table of Contents and Index>Bibliography Entry... and generate a special table “Bibliography” at end of document. This is not complicated but this site is not supposed to be a tutorial.
One final word: read the User Guide available for free download here. Make a pause with your document and read it. This is not wasted time. You’ll then write your document much faster and more reliably and you’ll be able to concentrate on your contents and not on the way to display it.
Remember that LO style architecture is akin to semantic marking. Define a style associated to a purpose, not to a visual effect. Once your document is completed, you play with style definitions to decorate your text without ever changing the wording. If your style collection fits your intent, achieving a nice presentation is a matter of a few minutes only.
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