$\frac{3}{7} * 2 = \frac{3 * 2}{7} = \frac{6}{7}$

$3 * \frac{1}{6} = \frac{3 * 1}{6} = \frac{3}{6} = \frac{1}{2}$

$9 * \frac{5}{6} = \frac{\overset{3}{\bcancel{9}} * 5}{\underset{2}{\bcancel{6}}} = \frac{3 * 5}{2} = \frac{15}{2} = 7\frac{1}{2}$

$\frac{2}{5} * 15 = \frac{2 * \overset{3}{\bcancel{15}}}{\underset{1}{\bcancel{5}}} = \frac{2 * 3}{1} = 6$

$\frac{1}{4} * 4 = \frac{4}{4} = 1$

$5 * \frac{1}{5} = \frac{5}{5} = 1$

$8 * \frac{3}{8} = \frac{\overset{1}{\bcancel{8}} * 3}{\underset{1}{\bcancel{8}}} = 3$

$6 * \frac{3}{4} = \frac{\overset{3}{\bcancel{6}} * 3}{\underset{2}{\bcancel{4}}} = \frac{3 * 3}{2} = \frac{9}{2} = 4\frac{1}{2}$