6. \(4\frac{2}{3}+5\frac{4}{7}\)

Общий знаменатель дробей — 21:

\(\frac{2}{3}=\frac{14}{21},\quad \frac{4}{7}=\frac{12}{21}\).

\(4\frac{2}{3}+5\frac{4}{7}=9+\frac{14}{21}+\frac{12}{21}=9\frac{26}{21}=10\frac{5}{21}\).

Ответ: \(10\frac{5}{21}\).