$$(19 \frac{1}{3} + 1 \frac{2}{3}) - (15 \frac{4}{7} - 12 \frac{5}{7}) = (19 + 1 + \frac{1}{3} + \frac{2}{3}) - (15 - 12 + \frac{4}{7} - \frac{5}{7}) = (20 + \frac{3}{3}) - (3 - \frac{1}{7}) = 21 - (3 - \frac{1}{7}) = 21 - 3 + \frac{1}{7} = 18 + \frac{1}{7} = 18 \frac{1}{7}$$.
**Ответ:** $$18 \frac{1}{7}$$