\[4\frac{4}{9}\ :2\frac{2}{3} = \frac{40}{9}\ :\frac{8}{3} = \frac{40}{9} \cdot \frac{3}{8} =\]
\[= \frac{8 \cdot 5 \cdot 3}{3 \cdot 3 \cdot 8} = \frac{5}{3} = 1\frac{2}{3}\]