Explanation:

If a number is divisible by both 8 and 3 then the number is divisible by 24 also.
So divisibility rule for 8 is last three digit should be divisible by 8
So, 536 and 576 are the last three digits divisible by 8, so we have to take least value hence, x = 3
Now, divisiblity rule for 3 is sum of the digits should be divisible by 3
So, 2+x+6+0+0+0+0+0+y+8=16+x+y+6 should be divisible by 3
16 + 3 +y=19+y should be divisible by 3
Now, least value for y which satisfied the condition is 2
So, x + y = 3 + 2 = 5