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\(\cfrac{4\sqrt{3}}{2-\sqrt {2}}\)-\(\cfrac{30}{4\sqrt{3}-\sqrt{18}}\)-\(\cfrac{\sqrt{18}}{3-2\sqrt{3}}\)
\(=\cfrac{4\sqrt{3}}{\sqrt{4}-\sqrt {2}}\)-\(\cfrac{30}{\sqrt{48}-\sqrt{18}}\)+\(\cfrac{\sqrt{18}}{2\sqrt{3}-3}\)
\(=\cfrac{4\sqrt{3}(\sqrt{4}+\sqrt {2})}{(\sqrt{4}-\sqrt {2})(\sqrt{4}+\sqrt {2})}\)-\(\cfrac{30(\sqrt{48}+\sqrt{18})}{(\sqrt{48}-\sqrt{18})(\sqrt{48}+\sqrt{18})}\)+\(\cfrac{\sqrt{18}(\sqrt{12}+\sqrt{9})}{(\sqrt{12}-\sqrt{9})(\sqrt{12}+\sqrt{9})}\)
\(=\cfrac{4\sqrt{3}(2+\sqrt {2})}{(\sqrt{4})^2-(\sqrt {2})^2}\)-\(\cfrac{30(4\sqrt{3}+3\sqrt{2})}{(\sqrt{48})^2-(\sqrt{18})^2}\)+\(\cfrac{3\sqrt{2}(2\sqrt{3}+3)}{(\sqrt{12})^2-(\sqrt{9})^2}\)
\(=\cfrac{4\sqrt{3}(2+\sqrt {2})}{4-2}\)-\(\cfrac{30(4\sqrt{3}+3\sqrt{2})}{48-18}\)+\(\cfrac{3\sqrt{2}(2\sqrt{3}+3)}{12-9}\)
\(=\cfrac{\cancel{4}2\sqrt{3}(2+\sqrt {2})}{\cancel2}\)-\(\cfrac{\cancel{30}(4\sqrt{3}+3\sqrt{2})}{\cancel{30}}\)+\(\cfrac{\cancel3\sqrt{2}(2\sqrt{3}+3)}{\cancel{3}}\)
\(=\cancel{4\sqrt3}+2\sqrt6-\cancel{4\sqrt3}-\cancel{3\sqrt2}+2\sqrt6+\cancel{3\sqrt2}\)
\(=4\sqrt6\) [Answer]