Answer
$240x^4y^2$
Work Step by Step
According to the Binomial Theorem we can obtain the $r+1$th term of the expansion of the binomial $(x+y)^n$ by the formula $_nC_rx^{n-r}y^r$.
Hence here it is: (by plugging in $n=6,r=2$ and $2x,y$: $_6C_2(2x)^{6-2}y^2=15\cdot16x^4y^2=240x^4y^2$