Explanation:

- To find two numbers with a mean of 12, they must add up to 24 (since the mean is sum/2).

- The difference between them is 6. If we call the numbers x and y, then x - y = 6.

- The pair of equations are: x + y = 24 and x - y = 6.

- Solving these gives x = 15 and y = 9.

Let's evaluate the options:

- Option 1: 2 and 22

- Sum: 24

- Mean: 12

- Difference: 20 (incorrect)

- Option 2: 14 and 10

- Sum: 24

- Mean: 12

- Difference: 4 (incorrect)

- Option 3: 15 and 9

- Sum: 24

- Mean: 12

- Difference: 6 (correct)

- Option 4: 3 and 24

- Sum: 27 (incorrect)

- Mean: 13.5 (incorrect)

- Difference: 21 (incorrect)