Answer :

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 
(3x²y²)(4xy³)²
(3x²y²)(4xy³)(4xy³)
(3x²y²)(16x²y^6)
48x^4y^8

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