a) $\left(\dfrac{2\sqrt3 - \sqrt6}{\sqrt8 - 2} - \dfrac{\sqrt{216}}{3}\right)\cdot\dfrac{1}{\sqrt6}$
$= \left(\dfrac{\sqrt6(\sqrt2 - 1)}{2(\sqrt2 - 1)} - \dfrac{2\sqrt2.3\sqrt3}{3}\right)\cdot\dfrac{1}{\sqrt6}$
$= \left(\dfrac{\sqrt6}{2} - 2\sqrt6\right)\cdot\dfrac{1}{\sqrt6}$
$= \dfrac{1}{2} - 2 = -\dfrac{3}{2}$
b) $\dfrac{\sqrt a + \sqrt b}{2\sqrt a - 2\sqrt b}- \dfrac{\sqrt a - \sqrt b}{2\sqrt a +2\sqrt b} - \dfrac{2b}{b - a}$
$= \dfrac{(\sqrt a + \sqrt b)^2}{2(\sqrt a - \sqrt b)(\sqrt a + \sqrt b)}- \dfrac{(\sqrt a - \sqrt b)^2}{2(\sqrt a +\sqrt b)(\sqrt a - \sqrt b)} + \dfrac{2b}{a - b}$
$= \dfrac{(\sqrt a + \sqrt b + \sqrt a - \sqrt b)(\sqrt a + \sqrt b - \sqrt a + \sqrt b)}{2(\sqrt a - \sqrt b)(\sqrt a + \sqrt b)} + \dfrac{2b}{a + b}$
$= \dfrac{2\sqrt a.2\sqrt b}{2(a - b)} +\dfrac{2b}{a - b}$
$= \dfrac{2b + 2\sqrt{ab}}{a - b}$
$= \dfrac{2\sqrt b(\sqrt b +\sqrt a)}{(\sqrt a - \sqrt b)(\sqrt a + \sqrt b)}$
$= \dfrac{2\sqrt b}{\sqrt a - \sqrt b}$
