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 $4^{2}$.
$$4\sqrt{2}-\sqrt{18}+\sqrt{8}$$
Factor $18=3^{2}\times 2$. Rewrite the square root of the product $\sqrt{3^{2}\times 2}$ as the product of square roots $\sqrt{3^{2}}\sqrt{2}$. Take the square root of $3^{2}$.
$$4\sqrt{2}-3\sqrt{2}+\sqrt{8}$$
Combine $4\sqrt{2}$ and $-3\sqrt{2}$ to get $\sqrt{2}$.
$$\sqrt{2}+\sqrt{8}$$
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 $2^{2}$.
$$\sqrt{2}+2\sqrt{2}$$
Combine $\sqrt{2}$ and $2\sqrt{2}$ to get $3\sqrt{2}$.
