Answer
$\dfrac{-7}{12+6\sqrt{11}}$
Work Step by Step
Multiplying by the conjugate of the numerator, then the rationalized-numerator form of the given expression, $
\dfrac{2-\sqrt{11}}{6}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{2-\sqrt{11}}{6}\cdot\dfrac{2+\sqrt{11}}{2+\sqrt{11}}
\\\\=
\dfrac{(2)^2-(\sqrt{11})^2}{6(2)+6\sqrt{11}}
\\\\=
\dfrac{4-11}{12+6\sqrt{11}}
\\\\=
\dfrac{-7}{12+6\sqrt{11}}
.\end{array}