6. Найдите значение выражения: \(\frac{4}{15}-\left(2-1\frac{1}{15}\right)\cdot\frac{4}{9}+\frac{2}{3}\).

\(2-1\frac1{15}=\frac{30}{15}-\frac{16}{15}=\frac{14}{15}\).

\(\frac4{15}-\frac{14}{15}\cdot\frac49+\frac23=\frac4{15}-\frac{56}{135}+\frac{90}{135}=\frac{36-56+90}{135}=\frac{70}{135}=\frac{14}{27}\).

Ответ: \(\frac{14}{27}\).