Answer
$4\sqrt{6}$
Work Step by Step
Using the properties of equality, the given expression, $
2\sqrt{24}-4\sqrt{54}+3\sqrt{96}
,$ simplifies to
\begin{array}{l}\require{cancel}
2\sqrt{4\cdot6}-4\sqrt{9\cdot6}+3\sqrt{16\cdot6}
\\\\=
2\sqrt{(2)^2\cdot6}-4\sqrt{(3)^2\cdot6}+3\sqrt{(4)^2\cdot6}
\\\\=
2(2)\sqrt{6}-4(3)\sqrt{6}+3(4)\sqrt{6}
\\\\=
4\sqrt{6}-12\sqrt{6}+12\sqrt{6}
\\\\=
4\sqrt{6}
.\end{array}
