Rationalize the denominator:

$\dfrac{2}{\sqrt{6}}$

(i) Rationalizing the denominator,

$\Rightarrow \dfrac{2}{\sqrt{6}} \times \dfrac{ \sqrt{6}}{\sqrt{6}} \\[1em] \Rightarrow \dfrac{2(\sqrt{6})}{(\sqrt{6})^2} \\[1em] \Rightarrow \dfrac{2\sqrt{6}}{6} \\[1em] \Rightarrow \dfrac{\sqrt{6}}{3}$

Hence, on rationalizing $\dfrac{2}{\sqrt{6}} = \dfrac{\sqrt{6}}{3}$.