Решение:

1) $$6\frac{8}{9}-3\frac{1}{2}+3\frac{1}{12}$$

$$6\frac{8}{9}-3\frac{1}{2}+3\frac{1}{12} = \frac{62}{9} - \frac{7}{2} + \frac{37}{12} =$$ $$ = \frac{62 \cdot 4}{9 \cdot 4} - \frac{7 \cdot 18}{2 \cdot 18} + \frac{37 \cdot 3}{12 \cdot 3} = \frac{248}{36} - \frac{126}{36} + \frac{111}{36} = \frac{248 - 126 + 111}{36} = \frac{233}{36} = 6\frac{17}{36}$$

Ответ: $$6\frac{17}{36}$$

2) $$8\frac{7}{9}+6\frac{2}{15}-4,3$$

$$8\frac{7}{9}+6\frac{2}{15}-4,3 = \frac{79}{9} + \frac{92}{15} - \frac{43}{10} =$$ $$= \frac{79 \cdot 50}{9 \cdot 50} + \frac{92 \cdot 30}{15 \cdot 30} - \frac{43 \cdot 45}{10 \cdot 45} = \frac{3950}{450} + \frac{2760}{450} - \frac{1935}{450} = \frac{3950 + 2760 - 1935}{450} = \frac{4775}{450} = \frac{191}{18} = 10\frac{11}{18}$$

Ответ: $$10\frac{11}{18}$$

3) $$(19\frac{5}{21}-8\frac{3}{14})-6\frac{5}{7}$$

$$(19\frac{5}{21}-8\frac{3}{14})-6\frac{5}{7} = (\frac{404}{21} - \frac{115}{14}) - \frac{47}{7} =$$ $$=(\frac{404 \cdot 2}{21 \cdot 2} - \frac{115 \cdot 3}{14 \cdot 3}) - \frac{47}{7} = (\frac{808}{42} - \frac{345}{42}) - \frac{47 \cdot 6}{7 \cdot 6} = \frac{808 - 345}{42} - \frac{282}{42} = $$ $$=\frac{463}{42} - \frac{282}{42} = \frac{463 - 282}{42} = \frac{181}{42} = 4\frac{13}{42}$$

Ответ: $$4\frac{13}{42}$$

4) $$(19-\frac{7}{8})-(4\frac{5}{6}-2\frac{8}{9})$$

$$(19-\frac{7}{8})-(4\frac{5}{6}-2\frac{8}{9}) = (\frac{152}{8} - \frac{7}{8}) - (\frac{29}{6} - \frac{26}{9}) = $$ $$= \frac{152 - 7}{8} - (\frac{29 \cdot 3}{6 \cdot 3} - \frac{26 \cdot 2}{9 \cdot 2}) = \frac{145}{8} - (\frac{87}{18} - \frac{52}{18}) = \frac{145}{8} - \frac{87-52}{18} = $$ $$=\frac{145}{8} - \frac{35}{18} = \frac{145 \cdot 9}{8 \cdot 9} - \frac{35 \cdot 4}{18 \cdot 4} = \frac{1305}{72} - \frac{140}{72} = \frac{1305 - 140}{72} = \frac{1165}{72} = 16\frac{13}{72}$$

Ответ: $$16\frac{13}{72}$$