1) $$5 \frac{7}{8} - 2 \frac{2}{3} + 4 \frac{5}{6} = \frac{47}{8} - \frac{8}{3} + \frac{29}{6} = \frac{47 \cdot 3}{8 \cdot 3} - \frac{8 \cdot 8}{3 \cdot 8} + \frac{29 \cdot 4}{6 \cdot 4} = \frac{141}{24} - \frac{64}{24} + \frac{116}{24} = \frac{141 - 64 + 116}{24} = \frac{193}{24} = 8 \frac{1}{24}$$
2) $$6 \frac{8}{15} + 4 \frac{5}{18} - 3.6 = \frac{98}{15} + \frac{77}{18} - \frac{36}{10} = \frac{98 \cdot 6}{15 \cdot 6} + \frac{77 \cdot 5}{18 \cdot 5} - \frac{36 \cdot 9}{10 \cdot 9} = \frac{588}{90} + \frac{385}{90} - \frac{324}{90} = \frac{588 + 385 - 324}{90} = \frac{649}{90} = 7 \frac{19}{90}$$
3) $$(4 \frac{3}{18} - 5 \frac{5}{18}) - 12 \frac{2}{9} = (\frac{75}{18} - \frac{95}{18}) - \frac{110}{9} = (\frac{-20}{18}) - \frac{110}{9} = \frac{-10}{9} - \frac{110}{9} = \frac{-120}{9} = -\frac{40}{3} = -13 \frac{1}{3}$$
4) $$(31 - 14 \frac{7}{15}) - (27 \frac{2}{3} - 19^3) = (31 - \frac{217}{15}) - (\frac{83}{3} - 6859) = (\frac{465}{15} - \frac{217}{15}) - (\frac{83}{3} - \frac{20577}{3}) = \frac{248}{15} - (\frac{-20494}{3}) = \frac{248}{15} + \frac{20494}{3} = \frac{248}{15} + \frac{102470}{15} = \frac{102718}{15} = 6847 \frac{13}{15}$$