$\sqrt{600}=\sqrt{6}\cdot\sqrt{100}=10\sqrt{6}$
$\sqrt{150}=\sqrt{25}\cdot\sqrt{6}=5\sqrt{6}$
$4\sqrt{54}=4{\sqrt{9}\cdot\sqrt{6}}=(4\cdot3)\sqrt{6}=12\sqrt{6}$
$6\sqrt{32}=6(\sqrt{16}\cdot\sqrt{2})=(6\cdot4)\sqrt{2}=24\sqrt{2}$
$3\sqrt{50}=3(\sqrt{25}\cdot\sqrt{2})=(3*5)\sqrt{2}=15\sqrt{2}$
$\sqrt{72}=\sqrt{36}\cdot\sqrt{2}=6\sqrt{2}$
$\frac{10\sqrt{6}+5\sqrt{6}+12\sqrt{6}}{24\sqrt{2}-15\sqrt{2}-6\sqrt{2}}=\frac{27\sqrt{6}}{3\sqrt{2}}=\frac{27}{3}\cdot\sqrt{\frac{6}{2}}=9\sqrt{3}$
$9+3=12$
12
