Решение:

a) $$\frac{4}{9} \cdot (-\frac{3}{8}) = -\frac{4 \cdot 3}{9 \cdot 8} = -\frac{12}{72} = -\frac{1}{6}$$

б) $$\frac{5}{6} - \frac{4}{9} : \frac{16}{21} = \frac{5}{6} - \frac{4}{9} \cdot \frac{21}{16} = \frac{5}{6} - \frac{4 \cdot 21}{9 \cdot 16} = \frac{5}{6} - \frac{84}{144} = \frac{5}{6} - \frac{7}{12} = \frac{10}{12} - \frac{7}{12} = \frac{3}{12} = \frac{1}{4}$$

Ответ: a) $$-\frac{1}{6}$$, б) $$\frac{1}{4}$$