${{\left( \frac{4}{15} \right)}^{3}}.{{\left( \frac{2}{3} \right)}^{-3}}.{{(0,8)}^{2}}.{{\left( \frac{2}{5} \right)}^{-4}}$

$={{\left( \frac{4}{15} \right)}^{3}}.{{\left( \frac{2}{3} \right)}^{-3}}.{{\left( \frac{4}{5} \right)}^{2}}.{{\left( \frac{2}{5} \right)}^{-4}}$

$={{\left( \frac{4}{15} \right)}^{3}}.{{\left( \frac{2}{3} \right)}^{-3}}.{{\left( \frac{4}{5} \right)}^{2}}.{{\left( \frac{2}{5} \right)}^{-4}}$ $=\frac{{{4}^{3}}{{.2}^{-3}}{{.4}^{2}}{{.2}^{-4}}}{{{15}^{3}}{{.3}^{-3}}{{.5}^{2}}{{.5}^{-4}}}$

$=\frac{{{4}^{5}}{{.2}^{-7}}}{{{15}^{3}}{{.15}^{-3}}{{.5}^{2}}{{.5}^{-1}}}$

$=\frac{{{2}^{10}}{{.2}^{-7}}}{{{15}^{0}}{{.5}^{1}}}$

$=\frac{{{2}^{3}}}{5}=\frac{8}{5}$