[tex]4\sqrt3\cdot10\sqrt{12}\cdot\sqrt6\cdot\sqrt2=(4\cdot10)\sqrt3\cdot\sqrt{12}\cdot\sqrt{6\cdot2}=40\sqrt3\cdot\sqrt{12}\cdot\sqrt{12}\\\\=40\sqrt3\cdot(\sqrt{12})^2=40\sqrt3\cdot12=\boxed{480\sqrt3}\\\\Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ for\ a\geq0\ and\ b\geq0\\\\(\sqrt{a})^2=a\ for\ a\geq0[/tex]
