Решение:

1. $$7 + \frac{8}{19} = \frac{7 \cdot 19}{19} + \frac{8}{19} = \frac{133}{19} + \frac{8}{19} = \frac{133 + 8}{19} = \frac{141}{19} = 7\frac{8}{19}$$
2. $$\frac{8}{68} + 9 = \frac{8}{68} + \frac{9 \cdot 68}{68} = \frac{8}{68} + \frac{612}{68} = \frac{8 + 612}{68} = \frac{620}{68} = \frac{155}{17} = 9\frac{2}{17}$$
3. $$3\frac{5}{16} + 4\frac{7}{16} = (3 + 4) + (\frac{5}{16} + \frac{7}{16}) = 7 + \frac{5 + 7}{16} = 7 + \frac{12}{16} = 7 + \frac{3}{4} = 7\frac{3}{4}$$
4. $$12\frac{8}{13} - 8\frac{4}{13} = (12 - 8) + (\frac{8}{13} - \frac{4}{13}) = 4 + \frac{8 - 4}{13} = 4 + \frac{4}{13} = 4\frac{4}{13}$$
5. $$5\frac{17}{21} - 3\frac{8}{21} + 4\frac{7}{21} = (5 - 3 + 4) + (\frac{17}{21} - \frac{8}{21} + \frac{7}{21}) = 6 + \frac{17 - 8 + 7}{21} = 6 + \frac{16}{21} = 6\frac{16}{21}$$
6. $$14\frac{8}{10} + 5\frac{1}{10} - 6\frac{7}{10} = (14 + 5 - 6) + (\frac{8}{10} + \frac{1}{10} - \frac{7}{10}) = 13 + \frac{8 + 1 - 7}{10} = 13 + \frac{2}{10} = 13 + \frac{1}{5} = 13\frac{1}{5}$$