[tex]24=4\cdot6\\96=16\cdot6\\\\2\sqrt6-4\sqrt{24}+\sqrt{96}=2\sqrt6-4\sqrt{4\cdot6}+\sqrt{16\cdot6}\\\\=2\sqrt6-4\cdot\sqrt4\cdot\sqrt6+\sqrt{16}\cdot\sqrt6=2\sqrt6-4\cdot2\cdot\sqrt6+4\cdot\sqrt6\\\\=2\sqrt6-8\sqrt6+4\sqrt6=(2-8+4)\sqrt6=-2\sqrt6\\\\\text{Answer:}\ -2\sqrt6\\\\\text{Used:}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b} [/tex]
