$$\left(1 + 6\frac{13}{14}\right) \cdot \left(\frac{1}{6} + \frac{8}{15}\right) = \left(1 + \frac{97}{14}\right) \cdot \left(\frac{5}{30} + \frac{16}{30}\right) = \left(\frac{14}{14} + \frac{97}{14}\right) \cdot \frac{21}{30} = \frac{111}{14} \cdot \frac{7}{10} = \frac{111}{2} \cdot \frac{1}{10} = \frac{111}{20} = 5\frac{11}{20}$$
Ответ: $$5\frac{11}{20}$$