\[\frac{3}{4} \cdot \frac{7}{8} - \frac{3}{4} \cdot \left( \frac{7}{8} - \frac{2}{3} \right) =\]
\[= \frac{3}{4} \cdot \left( \frac{7}{8} - \frac{7}{8} + \frac{2}{3} \right) = \frac{3}{4} \cdot \frac{2}{3} = \frac{1}{2}.\]