$\begin{array}{l}
4 - \left( {\frac{1}{3}:\frac{1}{2}} \right) \times \frac{2}{3}\\
= 4 - \left( {\frac{1}{3} \times \frac{2}{1}} \right) \times \frac{2}{3} = 4 - \frac{2}{3} \times \frac{2}{3}\\
= 4 - \frac{4}{9} = \frac{{36}}{9} - \frac{4}{9} = \frac{{32}}{9}
\end{array}$