$$ \left( \frac{4}{7} - \frac{1}{3} + \frac{5}{6} \right) \cdot 42 = \left( \frac{4 \cdot 6}{7 \cdot 6} - \frac{1 \cdot 14}{3 \cdot 14} + \frac{5 \cdot 7}{6 \cdot 7} \right) \cdot 42 = \left( \frac{24}{42} - \frac{14}{42} + \frac{35}{42} \right) \cdot 42 = \frac{24 - 14 + 35}{42} \cdot 42 = \frac{45}{42} \cdot 42 = 45 $$
Ответ: 45