$$\frac{5}{6}-\frac{4}{9}:\frac{16}{21} = \frac{5}{6} - \frac{4}{9} \cdot \frac{21}{16} = \frac{5}{6} - \frac{4 \cdot 21}{9 \cdot 16} = \frac{5}{6} - \frac{1 \cdot 7}{3 \cdot 4} = \frac{5}{6} - \frac{7}{12} = \frac{10}{12} - \frac{7}{12} = \frac{3}{12} = \frac{1}{4}$$
Ответ: $$\frac{1}{4}$$