Mean and variance of $X$ are $10$ and $2$, respectively.
Mean and variance of $Y$ are $20$ and $4$, respectively.
$$
\begin{aligned}
\operatorname{Var}(\mathrm{XY}) & =E\left[(X Y)^2\right]-(E[X Y])^2 \\
& =E\left[X^2 Y^2\right]-(E[X] E[Y])^2, \quad X \text { and } Y \text { are independent. } \\
& =E\left[X^2\right] E\left[Y^2\right]-E[X]^2 E[Y]^2, \quad X \text { and } Y \text { are independent. } \\
& =\left(\operatorname{Var}(X)+E[X]^2\right)\left(\operatorname{Var}(Y)+E[Y]^2\right)-E[X]^2 E[Y]^2 \\
& =\left(2+10^2\right)\left(4+20^2\right)-10^2 20^2 \\
& =(102 \times 404)-40000 \\
& =41208-40000 \\
& =1208
\end{aligned}
$$
