\[\sqrt{2b} - \frac{3}{2}\sqrt{32b} + 6\sqrt{\frac{8b}{9}} =\]
\[= \sqrt{2b} - \frac{3}{2} \cdot 4\sqrt{2b} + 6 \cdot \frac{2}{3}\sqrt{2b} =\]
\[= \sqrt{2b} - 6\sqrt{2b} + 4\sqrt{2b} = - \sqrt{2b}.\]