$$6 \frac{3}{7}-4 \frac{5}{7} = 5 \frac{10}{7} - 4 \frac{5}{7} = (5-4) + (\frac{10}{7} - \frac{5}{7}) = 1 + \frac{10-5}{7} = 1 + \frac{5}{7} = 1 \frac{5}{7}$$.
Ответ: $$1 \frac{5}{7}$$