#### Answer

$B = 45^{\circ}$

#### Work Step by Step

We can use the law of sines to find the angle $B$:
$\frac{a}{sin~A} = \frac{b}{sin~B}$
$sin~B = \frac{b~sin~A}{a}$
$sin~B = \frac{(2)~sin~(60^{\circ})}{\sqrt{6}}$
$sin~B = \frac{(2)~(\frac{\sqrt{3}}{2})}{\sqrt{6}}$
$sin~B = \frac{\sqrt{2}}{2}$
$B = arcsin(\frac{\sqrt{2}}{2})$
$B = 45^{\circ}$