$$4\frac{1}{6} \cdot 3\frac{2}{7} + 2\frac{5}{7} \cdot 4\frac{1}{6} = 4\frac{1}{6} \cdot \left(3\frac{2}{7}+2\frac{5}{7}\right) = 4\frac{1}{6} \cdot (3+2+\frac{2}{7}+\frac{5}{7}) = 4\frac{1}{6} \cdot (5+\frac{7}{7}) = 4\frac{1}{6} \cdot 6 = \frac{25}{6} \cdot 6 = 25$$
Ответ: 25