Using the binomial theorem we know that

(x - y)^4 = x^4 - 4*x^3*y + 6*x^2*y^2 - 4*x*y^3 + y^4

in our case we have to write [(x/3) - (2/y)]^4 that is

[(x/3) - (2/y)]^4 = (x/3)^4 - 4*(x/3)^3*(2/y) + 6*(x/3)^2*(2/y)^2 - 4*(x/3)*(2/y)^3 + (2/y)^4

[(x/3) - (2/y)]^4 = x^4/81 - (8/27)*x^3/y + (8/3)x^2/y^2 - (32/3) x/y^3 + 16/y^4