Factor $28=2^{2}\times 7$. Rewrite the square root of the product $\sqrt{2^{2}\times 7}$ as the product of square roots $\sqrt{2^{2}}\sqrt{7}$. Take the square root of $2^{2}$.
$$2\sqrt{7}-2\sqrt{18}+\sqrt{32}$$
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 $3^{2}$.
$$2\sqrt{7}-2\times 3\sqrt{2}+\sqrt{32}$$
Multiply $-2$ and $3$ to get $-6$.
$$2\sqrt{7}-6\sqrt{2}+\sqrt{32}$$
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 $4^{2}$.
$$2\sqrt{7}-6\sqrt{2}+4\sqrt{2}$$
Combine $-6\sqrt{2}$ and $4\sqrt{2}$ to get $-2\sqrt{2}$.
