\[\frac{6}{\sqrt{11} - 3} = \frac{6\left( \sqrt{11} + 3 \right)}{\left( \sqrt{11} - 3 \right)\left( \sqrt{11} + 3 \right)} =\]
\[= \frac{6\left( \sqrt{11} + 3 \right)}{11 - 9} = \frac{6\left( \sqrt{11} + 3 \right)}{2} =\]
\[= 3\left( \sqrt{11} + 3 \right)\]