Explanation:

Let’s break it down:

- For a number to be divisible by 88, it must be divisible by both 8 and 11.

- Divisibility by 8: the last three digits, 46B, must be a multiple of 8.

- Divisibility by 11: the difference between sum of alternate digits must be a multiple of 11.

Now, possible values for B (0–9) to make 46B divisible by 8:

- Try B=0: 460 ÷ 8 = 57.5

- Try B=4: 464 ÷ 8 = 58

- So, B = 4

Plugging in B=4, the number is 8A51464.

Now check divisibility by 11:

- Sum of digits at odd positions: 8 + 5 + 4 + 4 = 21

- Sum of digits at even positions: A + 1 + 6 = A + 7

- Difference = 21 - (A + 7) = 14 - A. This must be a multiple of 11.

- 14 - A = 11 ? A = 3

So AB = 34.

Let’s check the options:

1. 9

2. 15

3. 20

4. 12 (your answer)

None of the options match AB = 34.

— Here’s the thing: none of the provided options fit the right AB (34). Maybe there’s an error in the options, or a typo in the question. But, by calculation, the answer should be 34—so none of the options are right.