$$ 1\frac{1}{2} + (8 - 7\frac{2}{3}) : \frac{1}{2} - \frac{1}{6} = $$
$$ = \frac{3}{2} + (\frac{24}{3} - \frac{23}{3}) : \frac{1}{2} - \frac{1}{6} = $$
$$ = \frac{3}{2} + \frac{1}{3} : \frac{1}{2} - \frac{1}{6} = $$
$$ = \frac{3}{2} + \frac{1}{3} \cdot \frac{2}{1} - \frac{1}{6} = $$
$$ = \frac{3}{2} + \frac{2}{3} - \frac{1}{6} = $$
$$ = \frac{9}{6} + \frac{4}{6} - \frac{1}{6} = $$
$$ = \frac{13}{6} - \frac{1}{6} = $$
$$ = \frac{12}{6} = 2 $$
Ответ: 2