476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.

x - y - 3 = 0   ⟹ y = x - 3

(17 + x + y) = (17 + x + x - 3) = (2x + 14)

⟹ x= 2 or x = 8.

∴ x = 8 and y = 5.