$$4 \cdot (2\frac{1}{2} + 1\frac{3}{4}) - (6\frac{2}{3} + 4\frac{4}{5}) : 2 = 4 \cdot (\frac{5}{2} + \frac{7}{4}) - (\frac{20}{3} + \frac{24}{5}) : 2 = 4 \cdot (\frac{10}{4} + \frac{7}{4}) - (\frac{100}{15} + \frac{72}{15}) : 2 = 4 \cdot \frac{17}{4} - \frac{172}{15} : 2 = 17 - \frac{172}{15} \cdot \frac{1}{2} = 17 - \frac{86}{15} = \frac{255}{15} - \frac{86}{15} = \frac{169}{15} = 11\frac{4}{15}$$
Ответ: $$11\frac{4}{15}$$