Решение:
$[(7\frac{2}{3} - 6\frac{8}{15} \cdot \frac{5}{14}) : (8\frac{3}{4} \cdot \frac{2}{7} - 1\frac{1}{6}) + \frac{7}{18} : \frac{14}{27}](\frac{5}{6} - 0,75) \cdot \frac{20,4 \cdot 4,8 \cdot 6,5}{22,1 \cdot 1,2} = 9,5.$

$1) 6\frac{8}{15} \cdot \frac{5}{14} = \frac{98}{15} \cdot \frac{5}{14} = \frac{98 \cdot 5}{15 \cdot 14} = \frac{7 \cdot 1}{3 \cdot 1} = \frac{7}{3} = 2\frac{1}{3};$

$2) 7\frac{2}{3} - 2\frac{1}{3} = 7 + \frac{2}{3} - 2 - \frac{1}{3} = 7 - 2 + \frac{2 - 1}{3} = 5 + \frac{1}{3} = 5\frac{1}{3};$

$3) 8\frac{3}{4} \cdot \frac{2}{7} = \frac{35}{4} \cdot \frac{2}{7} = \frac{35 \cdot 2}{4 \cdot 7} = \frac{5 \cdot 1}{2 \cdot 1} = \frac{5}{2} = 2\frac{1}{2};$

$4) 2\frac{1}{2} - 1\frac{1}{6} = 2 + \frac{3}{6} - 1 - \frac{1}{6} = 2 - 1 + \frac{3 - 1}{6} = 1 + \frac{2}{6} = 1 + \frac{1}{3} = 1\frac{1}{3};$

$5) 5\frac{1}{3} : 1\frac{1}{3} = \frac{16}{3} \cdot \frac{3}{4} = \frac{16 \cdot 3}{3 \cdot 4} = \frac{4 \cdot 1}{1 \cdot 1} = 4;$

$6) \frac{7}{18} : \frac{14}{27} = \frac{7}{18} \cdot \frac{27}{14} = \frac{7 \cdot 27}{18 \cdot 14} = \frac{1 \cdot 3}{2 \cdot 2} = \frac{3}{4};$

$7) 4 + \frac{3}{4} = 4\frac{3}{4};$

$8) \frac{5}{6} - 0,75 = \frac{5}{6} - \frac{75}{100} = \frac{5}{6} - \frac{3}{4} = \frac{10}{12} - \frac{9}{12} = \frac{10 - 9}{12} = \frac{1}{12};$

$9) \frac{20,4 \cdot 4,8 \cdot 6,5}{22,1 \cdot 1,2} = \frac{20,4 \cdot 4 \cdot 5}{17 \cdot 1} = \frac{20,4 \cdot 20}{17} = \frac{408}{17} = 408 : 17 = 24;$

$10) 4\frac{3}{4} \cdot \frac{1}{12} = \frac{19}{4} \cdot \frac{1}{12} = \frac{19 \cdot 1}{4 \cdot 12} = \frac{19}{48};$

$11) \frac{19}{48} \cdot 24 = \frac{19}{2} \cdot 1 = \frac{19}{2} = 19 : 2 = 9,5.$
Ответ: 9,5.

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