6. \(1\frac{17}{28}\cdot\frac{14}{9}+\frac{14}{25}\cdot2\frac{5}{7}\)

Преобразуем смешанные числа: \(1\frac{17}{28}=\frac{45}{28}\), \(2\frac{5}{7}=\frac{19}{7}\).

\(\frac{45}{28}\cdot\frac{14}{9}=\frac{5}{2}\), \(\frac{14}{25}\cdot\frac{19}{7}=\frac{38}{25}\).

\(\frac{5}{2}+\frac{38}{25}=\frac{125}{50}+\frac{76}{50}=\frac{201}{50}=4\frac{1}{50}\).

Ответ: \(4\frac{1}{50}\).