When Mary is sixteen, she is four times as old as her brother, meaning her brother is 4 years old.
This means that the difference between their ages is 16-4 = 12 years.
No matter how old they get, this difference is always 12 years.
So, when Mary is twice the age of her brother, this means that her brother's age is equal to the difference in their ages. So her brother is 12 years old and Mary is 24 years old.
The answer is B.