Answer
$\frac{1}{4}$
Work Step by Step
$(\frac{7}{8} - \frac{1}{4}) - \frac{2}{3}(\frac{3}{4})^2$ = $(\frac{7}{8} - \frac{2}{8}) - \frac{2}{3}(\frac{9}{16})$ = $\frac{5}{8} - \frac{18}{48}$ = $\frac{5}{8} - \frac{3}{8}$ = $\frac{2}{8}$ = $\frac{1}{4}$