Explanation:

- The family consists of two grandparents, two parents, and four grandchildren.

- The average age of the grandparents is 67 years, so their total age is \(2 \times 67 = 134\) years.

- The average age of the parents is 35 years, so their total age is \(2 \times 35 = 70\) years.

- The average age of the grandchildren is 9 years, so their total age is \(4 \times 9 = 36\) years.

- To find the average age of the entire family, add the total ages of all members: \(134 + 70 + 36 = 240\) years.

- Divide the total age by the number of family members: \(\frac{240}{8} = 30\) years.

- The correct average age of the family is 30 years.