a) $6:\frac{1}{4} = \frac{6}{1} \times \frac{4}{1} = 24$
$7:\frac{2}{3} = \frac{7}{1} \times \frac{3}{2} = \frac{{21}}{2}$
$8:\frac{4}{5} = \frac{8}{1} \times \frac{5}{4} = \frac{{40}}{4} = 10$
b) $\frac{5}{9}:3 = \frac{5}{9} \times \frac{1}{3} = \frac{5}{{27}}$
$\frac{3}{4}:15 = \frac{3}{4} \times \frac{1}{{15}} = \frac{3}{{60}} = \frac{1}{{20}}$
$\frac{7}{6}:12 = \frac{7}{6} \times \frac{1}{{12}} = \frac{7}{{72}}$