Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$2\left(2\times 2\sqrt{2}+3\sqrt{32}\right)$$
Multiply $2$ and $2$ to get $4$.
$$2\left(4\sqrt{2}+3\sqrt{32}\right)$$
Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.
$$2\left(4\sqrt{2}+3\times 4\sqrt{2}\right)$$
Multiply $3$ and $4$ to get $12$.
$$2\left(4\sqrt{2}+12\sqrt{2}\right)$$
Combine $4\sqrt{2}$ and $12\sqrt{2}$ to get $16\sqrt{2}$.
