Explanation:

To find the greatest possible value of pq for the number 11p9q4 divisible by 24:

- A number is divisible by 24 if it is divisible by both 8 and 3.

- For divisibility by 8, the last three digits, 9q4, must be divisible by 8.

- For divisibility by 3, the sum of all digits, 1 + 1 + p + 9 + q + 4, must be divisible by 3.

- Calculate potential values of q satisfying 9q4 divisible by 8. Values can be 944, 984, and similar.

- Test each q to ensure that the corresponding sum for divisibility by 3 allows valid p values.

- Find the maximum value for pq among feasible p and q combinations.

After calculating:

- ?? 68 is the greatest possible value of pq as p = 6 and q = 8 satisfy divisibility conditions.

- Option 1: 56, Option 2: 68 , Option 3: 42, Option 4: 32