Desired would be a way, pixel exactly, to move an image using the cursor keys. In addition, an image may disappear to the top or bottom of the page during movement.
Edit your question to describe what you want to do. Don’t forget OS name and LO version.
Remember Writer is not a graphic application. It deals with text. If your purpose is to position a picture relative to text, say so and detail your positioning criteria. Moving a picture one-pixel distance does not make sense in a document application.
If the image is anchored To Page, To Paragraph, or to Character then select the image (or the frame if in a frame) by clicking on it. Use the arrow keys to move it by 10mm, Alt+arrow to move it by maybe 0.25 mm; for citizens of that country that was one of the founding signatories to the metric system, possibly 1/2 inch and 1/100th inch.
Note 1 if the paragraph shifts, for example, due to text being added above then the pictures anchored to that text will also shift. If the image is anchored to the page then the image will remain there even if the text that refers to it moves to another page.
Note 2 that if the image is anchored to paragraph or character, then if the image is moved above the anchor point the anchor point will jump up to the next available potential anchor point.
If the image is anchored As Character then horizontal movement can be made by alignment or tabs, potentially spaces but that introduces uncertainty. Vertical alignment to the baseline can be made by right-clicking the image, selecting Properties, in the dialog that opens, select the tab labelled Type, under Position, Vertical you have a choice of 3 settings or a distance that you specify from the bottom of the base line
I entirely agree with ajlittoz. If the precise position of images and text is the most important then Writer is unlikely to be the correct tool, maybe you should consider using Draw. Cheers, Al