Anita, two sisters, and three brothers - that is six people in all. If the mean of their ages is six years, then the sum of their ages is 36 years ( 6 years x 6 people).
Let's say that they are sextuplets so they are all six years old. In ten years from now, they will all be 16 years old. The sum of their ages will be 96 years (16 years x 6 people). The mean will be 16 years (96/6).
Example 2 below will be a double check of your answer.
Anita is 2 years old
Sister A is 3 years old
Sister B is 4 years old
Brother A is 8 years old
Brother B is 9 years old
Brother C is 20 years old
Add all their ages together, you will get a sum of 36. Dividing 36 years by 6 (people), you get a mean of 6.
In ten years,
Anita will be 12 years old
Sister A will be 13 years old
Sister B will be 14 years old
Brother A will be 18 years old
Brother B will be 19 years old
Brother C will be 20 years old.
Add all their ages together, you will get a sum of 96. Dividing 96 years by 6 (people), you get a mean of 16.
So your answer is, in ten years, their mean age is 16.