a) $12 \times (\frac{2}{3} - \frac{5}{6})^{2}$ = $12 \times (\frac{4}{6} - \frac{5}{6})^{2}$ = $12 \times (- \frac{1}{6})^{2}$ = $12 \times \frac{1}{36}$ = $\frac{1}{3}.$
b) $4 \times (\frac{-1}{2})^{3} - 2 \times (\frac{-1}{2})^{2} +3 \times (\frac{-1}{2}) +1$ = $4 \times \frac{-1}{8} - 2 \times \frac{1}{4} + \frac{-3}{2} +1 = \frac{-1}{2} - \frac{1}{2} + \frac{-3}{2} + \frac{2}{2} = \frac{-3}{2}$