a) $$4\frac{1}{6} \cdot (1\frac{1}{2} - \frac{3}{5}) + (\frac{3}{4} + \frac{5}{6}) \cdot 6$$

$$4\frac{1}{6} \cdot (1\frac{1}{2} - \frac{3}{5}) + (\frac{3}{4} + \frac{5}{6}) \cdot 6 = \frac{25}{6} \cdot (\frac{3}{2} - \frac{3}{5}) + (\frac{9}{12} + \frac{10}{12}) \cdot 6 = \frac{25}{6} \cdot (\frac{15}{10} - \frac{6}{10}) + \frac{19}{12} \cdot 6 = \frac{25}{6} \cdot \frac{9}{10} + \frac{19}{2} = \frac{5}{2} \cdot \frac{3}{2} + \frac{19}{2} = \frac{15}{4} + \frac{38}{4} = \frac{53}{4} = 13\frac{1}{4}$$ Ответ: $$13\frac{1}{4}$$