Решение:

1) $$2\frac{1}{4}:\frac{3}{8}:\frac{1}{2} = \frac{9}{4}:\frac{3}{8}:\frac{1}{2} = \frac{9}{4} \cdot \frac{8}{3} \cdot \frac{2}{1} = \frac{9 \cdot 8 \cdot 2}{4 \cdot 3 \cdot 1} = \frac{3 \cdot 2 \cdot 2}{1 \cdot 1 \cdot 1} = 12$$

Ответ: 12

2) $$2\frac{1}{4}:(\frac{3}{8}:\frac{1}{2}) = \frac{9}{4}:(\frac{3}{8} \cdot \frac{2}{1}) = \frac{9}{4}:\frac{6}{8} = \frac{9}{4}:\frac{3}{4} = \frac{9}{4} \cdot \frac{4}{3} = \frac{9 \cdot 4}{4 \cdot 3} = \frac{3}{1} = 3$$

Ответ: 3

3) $$(6\frac{3}{4}-5\frac{1}{8}:1\frac{9}{32}):2\frac{1}{5} = (\frac{27}{4}-\frac{41}{8}:\frac{41}{32}):\frac{11}{5} = (\frac{27}{4}-\frac{41}{8} \cdot \frac{32}{41}):\frac{11}{5} = (\frac{27}{4}-\frac{32}{8}):\frac{11}{5} = (\frac{27}{4}-4):\frac{11}{5} = (\frac{27}{4}-\frac{16}{4}):\frac{11}{5} = \frac{11}{4}:\frac{11}{5} = \frac{11}{4} \cdot \frac{5}{11} = \frac{5}{4} = 1\frac{1}{4}$$

Ответ: $$1\frac{1}{4}$$

4) $$(3\frac{1}{4}+2\frac{1}{6}):2\frac{3}{5}-\frac{2}{3}\cdot\frac{4}{9} = (\frac{13}{4}+ \frac{13}{6}):\frac{13}{5}-\frac{2}{3} \cdot \frac{4}{9} = (\frac{39}{12}+\frac{26}{12}):\frac{13}{5}-\frac{8}{27} = \frac{65}{12}:\frac{13}{5}-\frac{8}{27} = \frac{65}{12} \cdot \frac{5}{13}-\frac{8}{27} = \frac{5 \cdot 5}{12} - \frac{8}{27} = \frac{25}{12} - \frac{8}{27} = \frac{25 \cdot 9}{12 \cdot 9} - \frac{8 \cdot 4}{27 \cdot 4} = \frac{225}{108} - \frac{32}{108} = \frac{193}{108} = 1\frac{85}{108}$$

Ответ: $$1\frac{85}{108}$$