Explanation:

To determine if the number 32x4115y2 is divisible by 88, it must be divisible by both 8 and 11.

- Divisibility by 8: The last three digits, 5y2, must be divisible by 8. For this, try the smallest y values (0-9) until you find divisibility.

- Divisibility by 11: The difference between the sum of digits in odd positions and even positions must be a multiple of 11. Check these digits for divisors.

- Find smallest y that satisfies both conditions to get smallest x.

- Option 1: (4x - y = 31): Need to test if x and y fit the conditions for divisibility.

- Option 2: (4x - y = 20): Need to test similarly.

- Option 3: (4x - y = 1): Check as above.

- Option 4: (4x - y = 11): Evaluate for response accuracy with divisibility requirements.

Given these points, the option that works by testing y = 8 for 5y2 divisible by 8, and x = 2 making the number overall divisible by 88, resulting in 4x - y = 10.

Correct Answer: Option 4 (11)