Explanation:

- The average of ten numbers is 72, so the sum of all ten numbers is 720.

- The average of the first four numbers is 69, hence their sum is 276.

- The average of the next three numbers is 74, so their sum is 222.

- Let the 8th, 9th, and 10th numbers be \( x \), \( y \), and \( z \) respectively.

- From the information given:

- \( x = y + 6 \)

- \( x = z + 12 \)

- The sum of all ten numbers can be expressed as: 276 (first four) + 222 (next three) + \( x + y + z = 720 \).

- Solving for \( x, y, z \), they add up to 222.

- From:

- \( x + y + z = 222 \),

- \( x = y + 6 \), and

- \( x = z + 12 \),

- Substitute and solve:

- \( (y + 6) + y + ((y + 6) - 12) = 222 \)

- \( 3y = 222 \)

- \( y = 74 \), hence \( x = 80 \), \( z = 68 \).

- The average of the 8th and 9th numbers is \( \frac{80+74}{2} = 77 \).

Option 4: 77