Answer
$6\sqrt{3}-6\sqrt[]{2}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
3\sqrt{108}-2\sqrt[]{18}-3\sqrt{48}
\\=
3\sqrt{36\cdot3}-2\sqrt[]{9\cdot2}-3\sqrt{16\cdot3}
\\=
3\cdot6\sqrt{3}-2\cdot3\sqrt[]{2}-3\cdot4\sqrt{3}
\\=
18\sqrt{3}-6\sqrt[]{2}-12\sqrt{3}
\\=
(18\sqrt{3}-12\sqrt{3})-6\sqrt[]{2}
\\=
6\sqrt{3}-6\sqrt[]{2}
.\end{array}
