3.\newline4\frac{1}{6}-2\frac{5}{12}+(6\frac{3}{8}-4\frac{1}{4}+\frac{7}{16})\cdot\frac{5}{9}\cdot\frac{2}{15}

1. $$4\frac{1}{6} - 2\frac{5}{12} = \frac{25}{6} - \frac{29}{12} = \frac{25 \cdot 2}{6 \cdot 2} - \frac{29}{12} = \frac{50}{12} - \frac{29}{12} = \frac{21}{12} = \frac{7}{4}$$

2. $$6\frac{3}{8} - 4\frac{1}{4} + \frac{7}{16} = \frac{51}{8} - \frac{17}{4} + \frac{7}{16} = \frac{51 \cdot 2}{8 \cdot 2} - \frac{17 \cdot 4}{4 \cdot 4} + \frac{7}{16} = \frac{102}{16} - \frac{68}{16} + \frac{7}{16} = \frac{102 - 68 + 7}{16} = \frac{41}{16}$$

3. $$\frac{41}{16} \cdot \frac{5}{9} \cdot \frac{2}{15} = \frac{41}{16} \cdot \frac{1}{9} \cdot \frac{2}{3} = \frac{41 \cdot 1 \cdot 1}{8 \cdot 9 \cdot 3} = \frac{41}{72 \cdot 3} = \frac{41}{216}$$

4. $$\frac{7}{4} + \frac{41}{216} = \frac{7 \cdot 54}{4 \cdot 54} + \frac{41}{216} = \frac{378}{216} + \frac{41}{216} = \frac{378 + 41}{216} = \frac{419}{216} = 1\frac{203}{216}$$

Ответ: $$1\frac{203}{216}$$