$$3 \frac{3}{8} + 3 \frac{1}{5} - 4 \frac{1}{12} + 3 \frac{5}{6} = (3 + 3 - 4 + 3) + (\frac{3}{8} + \frac{1}{5} - \frac{1}{12} + \frac{5}{6}) = 5 + (\frac{3}{8} + \frac{1}{5} - \frac{1}{12} + \frac{5}{6}) = 5 + (\frac{45 + 24 - 10 + 100}{120}) = 5 + \frac{159}{120} = 5 + 1 \frac{39}{120} = 6 \frac{13}{40}$$
Ответ: $$6 \frac{13}{40}$$