$$ 4\frac{4}{11} \cdot \frac{5}{6} = \frac{48}{11} \cdot \frac{5}{6} = \frac{8}{11} \cdot \frac{5}{1} = \frac{40}{11} = 3\frac{7}{11} $$
Ответ: $$3\frac{7}{11}$$