Решение:

1. $$\frac{17}{12} + |-\frac{5}{6}|| = |\frac{17}{12} - \frac{5}{6}| = |\frac{17}{12} - \frac{10}{12}| = |\frac{7}{12}| = \frac{7}{12}$$
2. $$|-3\frac{1}{3}| - |-2\frac{6}{1}|| = |-\frac{10}{3}| - |-\frac{8}{1}| = \frac{10}{3} - \frac{8}{1} = \frac{10}{3} - \frac{24}{3} = -\frac{14}{3} = -4\frac{2}{3}$$

Ответ: 1) $$ \frac{7}{12}$$; 2) $$-4\frac{2}{3}$$