\[\frac{6 - \sqrt{12}}{\sqrt{12} - 2} = \frac{\sqrt{6}\left( \sqrt{6} - \sqrt{2} \right)}{\sqrt{2}\left( \sqrt{6} - \sqrt{2} \right)} =\]
\[= \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{\frac{6}{2}} = \sqrt{3}\]