Binomial Theorem

The question is: "What is the coefficient of a⁴b⁴ in the expansion of (a²/3 + 2b)⁶?"

In general: (x + y)⁶ = x⁶+6*x⁵*y+15*x⁴*y²+20*x³*y³+15*x²*y⁴+6*x*y⁵+y⁶

In your case x = a²/3 and y = 2b

I'm sure you can take it from here.

[6C2] X [a^2/3(First term of original binomial)]^(desired power(2)) X [2b(Second term of original binomial)]^(desired power(4)) 
(6C2 ) x (a^2/3)^2 x (2b)^4= 15 x a^4/9 x 16b^4=(15 x 16)/9a^4b^4=80/3a^4b^4