Explanation:

If sum of all the digits is divisible by 9 then the number is divisible by 9
Given number is 763X4Y2.
Given number is divisible by 9.
So, 7 + 6 + 3 + X + 4 + Y+ 2 = 9k
⇒ 22 + X + Y = 9k
It is clear that LHS is divisible by 9, if ?? + ?? =5, 14.
Now sum of X and Y in 5, then possible pairs are (1,4), (4, 1), (2, 3) (3, 2), (0, 5) and (5, 0).
When sum of X and Y is 11, then possible pairs are(5, 9), (9, 5), (6, 8), (8, 6) and (7, 7).
Total possible pairs are 11.