Question on 2-D Convolution
In addition to the above comment:

Show that the 2D Z-transforms of both sides are equal. 

Step-by-step: If $F(z_1, z_2)$ is the 2D Z-transform of $f(m,n)$, then what is the 2D Z-transform of 


$f(m-r, n)$?
$f(m-r, n-s)$?
$f(m, n) * g(m, n)$?
$f(m-r, n-s) * g(m, n)$?


(Yes, I realize that the 2D Z-transform may not be taught before this exam was presented, but it is a valid solution, nonetheless.)