Hello, Richay!

\(\displaystyle \L -3\sqrt{\frac{2}{3}}\,+\,2\sqrt{\frac{3}{2}}\)

Simplify each term:

\(\displaystyle \L\;\;-3\cdot\sqrt{\frac{2}{3}\cdot\frac{3}{3}}\:=\:-3\cdot\sqrt{\frac{6}{9}}\:=\:-3\cdot\frac{\sqrt{6}}{\sqrt{9}} \:=\;-\not{3}\cdot\frac{\sqrt{6}}{\not{3}}\:=\:-\sqrt{6}\)

\(\displaystyle \L\;\;2\cdot\sqrt{\frac{3}{2}\cdot\frac{2}{2}}\:=\:2\cdot\sqrt{\frac{6}{4}}\:=\:2\cdot\frac{\sqrt{6}}{\sqrt{4}}\:=\:\not{2}\cdot\frac{\sqrt{6}}{\not{2}}\:=\;\sqrt{6}\)

The problem becomes: \(\displaystyle \L\,-\sqrt{6}\,+\,\sqrt{6}\:=\:0\)