\(\left(\dfrac{\sqrt{216}}{3}-\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(\dfrac{6\sqrt{6}}{3}-\dfrac{\left(2\sqrt{3}-\sqrt{6}\right)\left(\sqrt{8}+2\right)}{\left(\sqrt{8}-2\right)\left(\sqrt{8}+2\right)}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(2\sqrt{6}-\dfrac{4\sqrt{6}+4\sqrt{3}-4\sqrt{3}-2\sqrt{6}}{4}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(2\sqrt{6}-\dfrac{2\sqrt{6}}{4}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(2\sqrt{6}-\dfrac{\sqrt{6}}{2}\right).\dfrac{1}{\sqrt{6}}.\\ =2\sqrt{6}.\dfrac{1}{\sqrt{6}}-\dfrac{\sqrt{6}}{2}.\dfrac{1}{\sqrt{6}}.\\ =2-\dfrac{1}{2}=\dfrac{3}{2}.\)
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