Ama's age is two-thirds that of her older sister. Four years ago,Ama's age was half the sisters.

How old is the sister?

a = 2/3 s

a-4 = 1/2 (s-4)
so that means
2/3 s - 4 = 1/2 s - 2
1/6 s = 2
s = 12