[tex]\displaystyle\\
3\sqrt{2} - 8\sqrt{6}: \Big(2 \sqrt{3} \Big) =\\\\
=3\sqrt{2} - \frac{8\sqrt{6}}{2 \sqrt{3}} =\\\\
=3\sqrt{2} - \frac{2\times 4\sqrt{3\times 2}}{2 \sqrt{3}} =\\\\
=3\sqrt{2} - \frac{2\sqrt{3} \times4\sqrt{2}}{2 \sqrt{3}} =\\\\
=3\sqrt{2} - 4\sqrt{2}= \boxed{\bf -\sqrt{2}}
[/tex]
