Answer
$-48+7\sqrt{6}$
Work Step by Step
Use the FOIL method, along with
$\sqrt{a}\times\sqrt{b}=\sqrt{ab},\qquad $
$\sqrt{a^{2}}=(\sqrt{a})^{2}=a$ (for positive a).
$F:\quad 3\sqrt{2}\times(2\sqrt{2})=3\times 2\times\sqrt{2\times 2}=6\times 2=12$
$O:\quad 3\sqrt{2}\times(5\sqrt{3})=3\times 5\times\sqrt{2\times 3}=15\sqrt{6}$
$I:\quad -4\sqrt{3}\times(2\sqrt{2})=-8\sqrt{2\times 3}=-8\sqrt{6}$
$L:\quad -4\sqrt{3}\times(5\sqrt{3})=-20\sqrt{3\times 3}=-20\times 3=-60$
Add like terms: (F+L)+(O+I)
$...$=$-48+7\sqrt{6}$
