Here are all the possible rolls with a 
red die and a green die:

(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) 

There are 36 possible rolls.  Now I 
will underline just those in which 
the number on the red exceeds the 
number showing on the green by exactly 
two:

(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)

There are 36 possible rolls.  So 
there are 4 possible rolls out of
the 36 which have that property.

Therefore the probability is  
which reduces to 

Edwin