98232x4567y divisible by 75

The values of x can be 3 and y can be 5 for the number to be divisible by 75. For divisibility by 75, the number should be divisible by 25 and 3. Last digit should be 5, and the sum of the digits should be a multiple of 3, this works when x is 3.

Looking at the prime factorization of 75 ,a number will be divisible by 75 if it is divisible by 25 and 3.For divisibility of number by 5 ^n, number formed by last n digits of the number should be divisible by 5^n(analogous rule applies to 2^n also ).For example when n=2 ,the number will be divisible by (5^2)25, if the number formed by last 2 digits is divisible by 25.They can be any of the following->25,50,75 ,00.In this case since penultimate digit is 7 so y=5 For divisibility by 3, the sum of digits should be divisible by 3 so x+51 should be divisible by 3.Hence x can be either of 3,6,9,0.