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Find the term that contains y^8 in the expansion of (2x+y^2)^6

Mathematics
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\[y ^{8}\] \[(2x+y^{2})^{6}\]
Binomial theorem ;)
Would it turn out to be \[y ^{8}=(y ^{2})^{U}\]

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Other answers:

My class hasn't covered logarithms yet, so I'm not sure if it's a guess 'n check type of thing.
Banging it out and multiplying will be extremely tedious. There's a simpler way to do it by using binomial theorem, but that is far too much explaining for now if you haven't already learned it. Does anyone have any other ideas?
I guess you could make an equation out of the exponents 8=2U...
\[\left(2 x+y^2\right)^6=64 x^6+192 x^5 y^2+240 x^4 y^4+160 x^3 y^6+60 x^2 y^8+12 x y^{10}+y^{12} \]

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