Вычислим:$$\frac{8}{21}:\frac{16}{27}-\frac{3}{14} = \frac{8}{21} \cdot \frac{27}{16} - \frac{3}{14} = \frac{1 \cdot 27}{7 \cdot 2} - \frac{3}{14} = \frac{27}{14} - \frac{3}{14} = \frac{27-3}{14} = \frac{24}{14} = \frac{12}{7} = 1\frac{5}{7}$$
Ответ: 1$$\frac{5}{7}$$