$${\frac{5}{16}} : {\frac{6}{8}} = {\frac{5}{16}} \cdot {\frac{8}{6}} = {\frac{5 \cdot 8}{16 \cdot 6}} = {\frac{5 \cdot 8}{2 \cdot 8 \cdot 6}} = {\frac{5}{12}}$$
Ответ: $$\frac{5}{12}$$