Решение:
$$\frac{8}{9} - \frac{3}{8} : \frac{27}{28} = \frac{8}{9} - \frac{3}{8} \times \frac{28}{27} = \frac{8}{9} - \frac{3 \times 28}{8 \times 27} = \frac{8}{9} - \frac{1 \times 7}{2 \times 9} = \frac{8}{9} - \frac{7}{18} = \frac{16}{18} - \frac{7}{18} = \frac{9}{18} = \frac{1}{2}$$
Ответ: $$\frac{1}{2}$$