Here are all possible rolls, the only sums of rolls divisible by 4
are 4, 8, and 12. The rolls with those sums are colored red below:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

1. Count the red ones.  That will be the numerator.
2. Count them all, red or black.  That will be the denominator.
3. Reduce the fraction, if it can be reduced. 

Edwin