X 0 1 2 _________________________ 0 | 16/36 8/36 1/36 | Y 1 | 8/36 2/36 0 | 2 | 1/36 0 0 | __|___________________|_ |
This is the table I would have made. If X = 2, then that means that both the dice had a 1, and there is only one scenario out of 36 where both 1's show up. If X=1 and Y=0, then that means only one 1 showed up, and the other dice was not a 4 or a 1. There are 8 unique cases of such. (You can mirror these two for Y=2 and Y=1,X=0. For X=1 and Y=1, that means one 1 showed up and one 4 showed up. There are two possible scenarios for that. For X=0 and Y=0, that means no 1's showed up and no 4's showed up. There are only 4 other sides to each of the die, so 4*4 = 16.
Below are the 36 possible die rolls: 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