a) What CPU?

b) What OS?

c) Is this a stock GUI like Windows or X, or a roll your own project where you're doing all the graphics yourself the hard way?

In dos with masm

You will need to study the various functions available in the bios int 10h. You won't find any ready made functions to "drag and drop" (I don't think); you will just have to keep redrawing the rectangle as the mouse moves; each time saving the original screen contents so that they can be restored each time the mouse moves to a new location.