Решение:
1. \(\frac{8}{21} : \frac{16}{27} = \frac{8}{21} \cdot \frac{27}{16} = \frac{8 \cdot 27}{21 \cdot 16} = \frac{1 \cdot 9}{7 \cdot 2} = \frac{9}{14}\)
2. \(\frac{9}{14} - \frac{3}{14} = \frac{9-3}{14} = \frac{6}{14} = \frac{3}{7}\)
Ответ: \(\frac{3}{7}\)