Ответ:

\(\frac{3}{4}\cdot\frac{2}{9}=\frac{1}{6}\).

\(\frac{1}{6}+\frac{5}{8}=\frac{4}{24}+\frac{15}{24}=\frac{19}{24}\).

\(\frac{19}{24}\cdot\frac{2}{5}=\frac{19}{60}\).

Ответ: \(\frac{19}{60}\).