\(4\frac{1}{3}\cdot\left(5\frac{1}{5}+2\frac{1}{2}+6\frac{1}{5}\right)\)

\(4\frac{1}{3}=\frac{13}{3}\), а \(5\frac{1}{5}+2\frac{1}{2}+6\frac{1}{5}=\frac{26}{5}+\frac{5}{2}+\frac{31}{5}=\frac{62}{5}\).

\(\frac{13}{3}\cdot\frac{62}{5}=\frac{806}{15}=53\frac{11}{15}\).

Ответ: \(53\frac{11}{15}\).