$a)$ $3\sqrt{8}-4\sqrt{18}+2\sqrt{50}$

$=3\sqrt{2^2.2}-4\sqrt{3^2.2}+2\sqrt{5^2.2}$

$=3.2\sqrt{2}-4.3\sqrt{2}+2.5\sqrt{2}$

$=6\sqrt{2}-12\sqrt{2}+10\sqrt{2}$

$=4\sqrt{2}$

$b)$ $\dfrac{a\sqrt{b}}{a}-\dfrac{1}{a}\sqrt{a^2b}+\dfrac{2}{3b}\sqrt{9ab^3}$ $(a; b>0$)

$=\sqrt{ab}-\dfrac{1}{a}.a\sqrt{b}+\dfrac{2}{3b}\sqrt{ab.(3b)^2}$

$=\sqrt{ab}-\dfrac{1}{a}.a\sqrt{b}+\dfrac{2}{3b}.3b.\sqrt{ab}$

$=\sqrt{ab}-\sqrt{b}+2\sqrt{ab}$

$=3\sqrt{ab}-\sqrt{b}$