$$3\frac{4}{7} \cdot 9\frac{16}{17} + 3\frac{4}{7} \cdot 7\frac{1}{17} = 3\frac{4}{7} \cdot (9\frac{16}{17} + 7\frac{1}{17}) = 3\frac{4}{7} \cdot (9 + 7 + \frac{16}{17} + \frac{1}{17}) = 3\frac{4}{7} \cdot (16 + \frac{17}{17}) = 3\frac{4}{7} \cdot (16 + 1) = 3\frac{4}{7} \cdot 17 = \frac{3 \cdot 7 + 4}{7} \cdot 17 = \frac{25}{7} \cdot 17 = \frac{425}{7} = 60\frac{5}{7}$$
Ответ: $$60\frac{5}{7}$$