First, I would solve the second parenthesis.
(4xy^3)^2
Distribute
(4^2 x^2 y^6)
4 x 4 = 16
Now, combine like terms
3x^2 x 4x^2 = 12x^4
y^2 x y^6 = y^12
So, the answer would be 12x^4 y^12
Hmm actually I'm not sure. I did this about two years ago so I don't really remember sorry if this is really wrong
