1) $$7 + \frac{8}{19} = 7\frac{8}{19}$$.
2) $$6\frac{8}{19} + 9 = (6 + 9) + \frac{8}{19} = 15 + \frac{8}{19} = 15\frac{8}{19}$$.
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) $$14\frac{8}{10} + 5\frac{1}{10} - 6\frac{7}{10} = (14 + 5 - 6) + (\frac{8}{10} + \frac{1}{10} - \frac{7}{10}) = 13 + \frac{8 + 1 - 7}{10} = 13 + \frac{2}{10} = 13 + \frac{1}{5} = 13\frac{1}{5}$$.
Ответ: 1) $$7\frac{8}{19}$$; 2) $$15\frac{8}{19}$$; 3) $$7\frac{3}{4}$$; 4) $$4\frac{4}{13}$$; 5) $$6\frac{16}{21}$$; 6) $$13\frac{1}{5}$$