How to re-arrange the column headings?

Folder: …My Docs;
Column headings > FILE | TYPE | SIZE | DATE etc.
Change to > FILE | DATE | TYPE | SIZE |

I believe Drag … HOW?

Is this a question about the Windows file manager ‘explorer.exe’?
Best look for information about MS windows then.
The dialogues used by LibO for Open/Save can be either those from the operating system (you likely chose) or those coming with LibO itself (nearly independent of the OS). For the second case I do not know a way to change the order.

Provided that you mean to move columns in the (Windows) File Explorer: Yes, drag the column headings that you want to move to where you want them. Works in Windows 10.

On Writer there is no easy way. In fact, you can end up overwriting one of the columns. See here for more details and related bug reports:

How can I move a column in a Writer table?

(Supposing the question was about the Open/Save dialogues.)

The default/most chosen setting should be that > ‘Tools’ > ‘Options’ > ‘LibreOffice’ > ‘General’ > ‘Open/Save Dialogue Boxes’ > ‘Use LibreOffice dialogue boxes’ is not checked. In this case dialogues supplied by the file manager of the operating system are used.

In case of ‘Windows’ (recent versions): The information how to display the folder’s contents (Symbols?, Details? …; order, width per header if ‘Details’) is customisable and saved per folder. For any folder there is an option to apply the settings also to all the subfolders (as long as not again customised differently). I do not know a way to use LibreOffice to force a specific view on all the folders showing when Open/Save is active.