Hello!
As a starting point, so we are on the same playing field, do you understand the difference between DVI-A, DVI-D, and DVI-I, all the difference between single link and duel link? You can read about them here:
All About DVI
What you are showing in your picture is a DVI-D Dual Link to VGA adapter. This adapter will take in a digital DVI input, convert, and output it to VGA, and so will be only that way around.
What exactly were you trying to do? With a few conversion cables, and with some difficulty, it is possible to connect a VGA graphics card to a DVI monitor, although my understanding of this is that it cannot work.
Richard