Let the number of left-handed boys be . Since there are four times as many right-handed boys, the number of right-handed boys is . Since there are twice as many left-handed girls as left-handed boys, and there are left-handed boys, there are left-handed girls. We place all of this in a Venn diagram:

We also know that half the girls on the team are left-handed. Since there are left-handed girls, there are also right-handed girls.

There are a total of

36=2x+x+4x+2x=9x

people on the team, so x=4. We are trying to find the number of right-handed boys. This number is

4x=4*4=16