Answer
$60x^4y^2$
Work Step by Step
Calculate the third term for $(x+2y)^{6}$ by using General formula such as:$(m+n)^r=\displaystyle \binom{r}{k}m^{r-k}n^k$
and $\displaystyle \binom{r}{k}=\dfrac{r!}{k!(r-k)!}$
This implies,
$(x+2y)^{6}=\displaystyle \binom{6}{2}(2x)^{6-2}(2y)^2$
or,$=\dfrac{6!}{2!(6-2)!}(x)^{4}(2)^2y^2$
or, $=(4)\dfrac{6 \times 5 \times 4!}{2 \times 1(4!)}(x)^{4}(y)^2$
or, $=60x^4y^2$
