6. \(\frac{9}{2}\cdot\left(\frac{8}{3}-\frac{3}{10}\right)\cdot\frac{4}{5}=\)

\(\frac{8}{3}-\frac{3}{10}=\frac{80-9}{30}=\frac{71}{30}\).

\(\frac{9}{2}\cdot\frac{71}{30}\cdot\frac{4}{5}=\frac{213}{20}=10\frac{13}{20}\).

Ответ: \(10\frac{13}{20}\).