$\begin{align}  & \text{Note: }{{a}^{2}}-{{b}^{2}}=(a-b)(a+b)\text{    }Difference\text{ }of\text{ }two\text{ }squares \\ & {{(\sqrt{6}+2)}^{2}}-{{(\sqrt{6}-2)}^{2}}=\left[ (\sqrt{6}+2)+(\sqrt{6}-2) \right]\left[ (\sqrt{6}+2)-(\sqrt{6}-2) \right] \\ & {{(\sqrt{6}+2)}^{2}}-{{(\sqrt{6}-2)}^{2}}=\left[ \sqrt{6}+2+\sqrt{6}-2 \right]\left[ \sqrt{6}+2-\sqrt{6}+2 \right] \\ & {{(\sqrt{6}+2)}^{2}}-{{(\sqrt{6}-2)}^{2}}=2\sqrt{6}\times 4 \\ & {{(\sqrt{6}+2)}^{2}}-{{(\sqrt{6}-2)}^{2}}=8\sqrt{6} \\\end{align}$