The question is: "*What is the coefficient of a*^{4}b^{4} in the expansion of (a^{2}/3 + 2b)^{6}?"

In general: (x + y)^{6} = x^{6}+6*x^{5}*y+15*x^{4}*y^{2}+20*x^{3}*y^{3}+15*x^{2}*y^{4}+6*x*y^{5}+y^{6}

In your case x = a^{2}/3 and y = 2b

I'm sure you can take it from here.