#### Answer

$12\sqrt[]{2}-12\sqrt{3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[]{6}(2\sqrt[]{12}-3\sqrt{8})
,$ simplifies to
\begin{array}{l}\require{cancel}
2\sqrt[]{6(12)}-3\sqrt{6(8})
\\\\=
2\sqrt[]{6(6\cdot2)}-3\sqrt{(2\cdot3)(8})
\\\\=
2\sqrt[]{(6)^2\cdot2}-3\sqrt{16\cdot3}
\\\\=
2\cdot6\sqrt[]{2}-3\sqrt{(4)^2\cdot3}
\\\\=
2\cdot6\sqrt[]{2}-3(4)\sqrt{3}
\\\\=
12\sqrt[]{2}-12\sqrt{3}
.\end{array}