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[tex]2\sqrt3\cdot\sqrt{18}=2\sqrt{3\cdot18}=2\sqrt{54}=\\\\=2\sqrt{9\cdot6}=2\sqrt{3^2\cdot6}=2\cdot3\sqrt6=\boxed{6\sqrt6}[/tex]
[tex]2\sqrt{3}\cdot\sqrt{18} = 2\sqrt{3}\cdot\sqrt{9\cdot2} = 2\sqrt{3}\cdot3\sqrt{2} = 6\sqrt{3\cdot2} = 6\sqrt{6}[/tex]