Answer
The factor is $\frac{\sqrt 6}{\sqrt 6}$.
After rationalizing: $\frac{2\sqrt 6}{3}$
Work Step by Step
The appropriate factor here is $\frac{\sqrt 6}{\sqrt 6}$.
$\frac{4}{\sqrt {6}}=\frac{4}{\sqrt {6}}\times\frac{\sqrt 6}{\sqrt 6}=\frac{4\sqrt {6}}{6}=\frac{2\sqrt 6}{3}$