If I have an image size 3 inches x 4 inches stored in my computer with the resolution of 1200 dpi.
What is the appropriate compression factor, if this image has to be displayed on a screen of size 6 inches by 8 inches having a resolution of 200 lines per inch and 200 dots per line.
Calculate how many dots are in the original image, and how many can be displayed on the screen. You don't need more than you can display. Compression factor uses the ratio of those numbers of dots. You should be able to figure it out!
You should be treating the display as one vertical pixel per line.
You should be able to calculate the resizing easily enough. You are doubling the horizontal and vertical sizes, which would stretch the 1200 dpi out to 600 dpi. The display is only capable of 200 dpi so you need to subsample by a factor of 3.