find the values of Y of the following equation :

(8^x)^y 1/32^y = 4

Assuming you mean (8^y)^y, we have

8^y^2 = 2^3y^2
1/32^y = 2^-5y
4 = 2^2

3y^2-5y = 2
y = 2 or -1/3