3.23 878 4

$$\frac{3}{8} \cdot 2\frac{2}{7} - 4\frac{2}{3} = \frac{3}{8} \cdot \frac{2 \cdot 7 + 2}{7} - \frac{4 \cdot 3 + 2}{3} = \frac{3}{8} \cdot \frac{14 + 2}{7} - \frac{12 + 2}{3} = \frac{3}{8} \cdot \frac{16}{7} - \frac{14}{3} = \frac{3 \cdot 16}{8 \cdot 7} - \frac{14}{3} = \frac{3 \cdot 2}{7} - \frac{14}{3} = \frac{6}{7} - \frac{14}{3} = \frac{6 \cdot 3}{7 \cdot 3} - \frac{14 \cdot 7}{3 \cdot 7} = \frac{18}{21} - \frac{98}{21} = \frac{18 - 98}{21} = \frac{-80}{21} = -3\frac{17}{21}$$

Ответ: $$-3\frac{17}{21}$$