Answer
$$\frac{4+\sqrt{10}}{3}$$
Work Step by Step
To rationalize the denominator multiply by $\frac{4+\sqrt{10}} {4+\sqrt{10}}$ ($=1$)
$$\frac{2}{4-\sqrt{10}}=\bigg(\frac{2}{4-\sqrt{10}}\bigg)\bigg(\frac{4+\sqrt{10}} {4+\sqrt{10}}\bigg)$$
$$=\frac{2(4+\sqrt{10})}{16-10}=\frac{2(4+\sqrt{10})}{6}=\frac{4+\sqrt{10}}{3}$$
