How Many Cherries

Let the number collected by the boy be $y$ , then $2y+y=108$ . If the situation were that they collected equal number of cherries, they would both pick $\frac{1}{2} 108 = 54$ cherries. But because the girl has collected twice as much, we have three parts now, where $\frac{2}{3}$ of the collected cherries were the girl's $\implies$ the boy had $\frac{1}{3} 108 = 36$ cherries. We obtain $36 \times 2 = \boxed{72}$ cherries collected by the girl.