Say there is a following image. I'd like to fill the part with letters ry with white color (ry is an example for a question). It can be done by the following command:
mogrify -fill white -draw "rectangle <coordinates, size>" *.jpg
I'd like to know how do I "convert" selection of ry part of the image from GIMP to be understood by imagemagick? In other words, given selection made in GIMP, what values do I use instead of <coordinates, size>?

As per request, I show how GIMP coordinates look:

On a side node, I use the following command to crop image using mogrify when using coordinates from GIMP mogrify -crop 0x0+4248+6336 *.jpg
where 0 -> position from left, 0 -> position from right 4248 -> size from left, 6336 -> size from right Perhaps this helps.
If I assume your coordinates are top-left corner, width and height, then there are two ways to fill white in Imagemagick. The first is to overlay a white image. The second is to draw a white rectangle.
Overlay White Image:
Draw White Rectangle: