$$6\frac{1}{4}\cdot 8-3\frac{2}{3}\cdot 5\frac{1}{2}+2\frac{2}{5}\cdot 4\frac{7}{12} = \frac{25}{4} \cdot \frac{8}{1} - \frac{11}{3} \cdot \frac{11}{2} + \frac{12}{5} \cdot \frac{55}{12} =$$
$$ = \frac{25 \cdot 8}{4 \cdot 1} - \frac{11 \cdot 11}{3 \cdot 2} + \frac{12 \cdot 55}{5 \cdot 12} = \frac{200}{4} - \frac{121}{6} + \frac{660}{60} = $$
$$ = 50 - \frac{121}{6} + 11 = 61 - \frac{121}{6} = \frac{61 \cdot 6 - 121}{6} = \frac{366 - 121}{6} = \frac{245}{6} = 40 \frac{5}{6}$$
Ответ: $$40 \frac{5}{6}$$