Explanation:

- To find a number divisible by both 7 and 3, we need it to be divisible by 21 (since 7 × 3 = 21).

- We are looking for the largest two-digit number that fits this rule.

- Option 1: 91

- 91 ÷ 7 = 13 (divisible)

- 91 ÷ 3 ˜ 30.33 (not divisible)

- Option 2: 96

- 96 ÷ 7 ˜ 13.71 (not divisible)

- 96 ÷ 3 = 32 (divisible)

- Option 3: 63

- 63 ÷ 7 = 9 (divisible)

- 63 ÷ 3 = 21 (divisible)

- Not the largest two-digit number.

- Option 4: 84

- 84 ÷ 7 = 12 (divisible)

- 84 ÷ 3 = 28 (divisible)

- Correct Answer: 84 is divisible by both.