$$(\frac{4}{7} - \frac{1}{3} + \frac{5}{6}) \cdot 42 = (\frac{4 \cdot 6 - 1 \cdot 14 + 5 \cdot 7}{42}) \cdot 42 = \frac{24 - 14 + 35}{42} \cdot 42 = 24 - 14 + 35 = 10 + 35 = 45$$
Ответ: $$45$$