Factor $128=8^{2}\times 2$. Rewrite the square root of the product $\sqrt{8^{2}\times 2}$ as the product of square roots $\sqrt{8^{2}}\sqrt{2}$. Take the square root of $8^{2}$.
$$8\sqrt{2}-\sqrt{32}$$
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 $4^{2}$.
$$8\sqrt{2}-4\sqrt{2}$$
Combine $8\sqrt{2}$ and $-4\sqrt{2}$ to get $4\sqrt{2}$.
