a) $\frac{5}{9} + \frac{4}{3} = \frac{5}{9} + \frac{{12}}{9} = \frac{{17}}{{19}}$
b) $\frac{5}{6} - \frac{2}{3} = \frac{5}{6} - \frac{4}{6} = \frac{1}{6}$
c) $\frac{{15}}{8} \times \frac{4}{5} = \frac{{60}}{{40}} = \frac{3}{2}$
d) $\frac{6}{7}:\frac{8}{{14}} = \frac{6}{7} \times \frac{{14}}{8} = \frac{{84}}{{56}} = \frac{3}{2}$