Explanation:

Let’s break this down step by step.

- We’re told 476 0 (let’s assume that’s a typo and they mean 476 _ * _0—"0" is a digit to find) is divisible by both 3 and 11.

- Divisibility by 3: sum of the digits must be a multiple of 3.

- Divisibility by 11: alternating sum (subtract one digit, add the next, etc.) must be a multiple of 11.

- The hundredth and tenth places in 476_0 are _ and 0.

- The options are giving you pairs of digits for those places. For each, we need the digits you put in to make it work.

- Let’s try each option:

Option 1: 2 and 3

47623

Sum: 4+7+6+2+3=22 (not divisible by 3)

Option 2: 3 and 2

47632

Sum: 22 (again, not divisible by 3)

Option 3: 5 and 8

47658

Sum: 4+7+6+5+8=30 (divisible by 3);

Alternating sum for 11: 4-7+6-5+8 = 6 (not divisible by 11)

Option 4: 8 and 5

47685

Sum: 4+7+6+8+5=30 (divisible by 3)

Alternating sum: 4-7+6-8+5 = 0 (divisible by 11)

The right answer is Option 4: 8 and 5.

What this really means is, the only pair that works for both divisibility rules is 8 (hundreds), 5 (tens).

The other options:

- Either don’t get you a sum divisible by 3, or

- Fail the alternating 11 rule.

- Option 4 is the only pair that actually fits the conditions.