6) Вычислите: \(\frac{8}{25}\cdot\frac{45}{12} : \left(1\frac{1}{14}-1\frac{1}{21}\right)\cdot\frac{5}{27}+5\frac{2}{3}\).

\[1\frac{1}{14}-1\frac{1}{21}=\frac{15}{14}-\frac{22}{21}=\frac{45-44}{42}=\frac{1}{42}.\]

\[\frac{8}{25}\cdot\frac{45}{12}:\frac{1}{42}\cdot\frac{5}{27}+5\frac{2}{3}=\frac{8}{25}\cdot\frac{15}{4}\cdot42\cdot\frac{5}{27}+\frac{17}{3}.\]

\[\frac{8}{25}\cdot\frac{15}{4}\cdot42\cdot\frac{5}{27}=\frac{56}{9}.\]

\[\frac{56}{9}+\frac{17}{3}=\frac{56}{9}+\frac{51}{9}=\frac{107}{9}=11\frac{8}{9}.\]

Ответ: \(11\frac{8}{9}\).