To subtract the fractions in the provided exercise, we follow the basic rule of finding a common denominator when necessary and then performing the subtraction. Let’s work through each of the problems:

1. \(\frac{1}{6} - \frac{5}{6} = \frac{1 - 5}{6} = \frac{-4}{6} = \frac{-2}{3}\)

2. \(\frac{6}{13} - \frac{14}{39} = \frac{6 \cdot 3}{13 \cdot 3} - \frac{14}{39} = \frac{18}{39} - \frac{14}{39} = \frac{4}{39}\)

3. \(\frac{4}{5} - \frac{4}{-18} = \frac{4}{5} + \frac{4}{18} = \frac{4}{5} + \frac{2}{9} = \frac{4 \cdot 9 + 2 \cdot 5}{5 \cdot 9} = \frac{36 + 10}{45} = \frac{46}{45}\)

4. \(\frac{7}{21} - \frac{9}{36} = \frac{1}{3} - \frac{1}{4} = \frac{4 - 3}{12} = \frac{1}{12}\)

5. \(-\frac{12}{18} - \frac{21}{35} = -\frac{2}{3} - \frac{3}{5} = -\frac{10 + 9}{15} = -\frac{19}{15}\)

6. \(-\frac{3}{21} - \frac{6}{42} = -\frac{1}{7} - \frac{1}{7} = -\frac{2}{7}\)

7. \(-\frac{18}{24} - \frac{15}{24} = -\frac{33}{24} = -\frac{11}{8}\)

8. \(\frac{1}{2} - \frac{6}{24} = \frac{12}{24} - \frac{6}{24} = \frac{6}{24} = \frac{1}{4}\)

9. \(\frac{3}{5} - \frac{7}{4} = \frac{12 - 35}{20} = \frac{-23}{20}\)

10. \((-2) - (-\frac{5}{8}) = -2 + \frac{5}{8} = \frac{-16 + 5}{8} = \frac{-11}{8}\)

11. \(-\frac{1}{8} - \frac{5}{9} = -\frac{9 + 40}{72} = -\frac{49}{72}\)

12. \(\frac{4}{13} - (-\frac{12}{39}) = \frac{4}{13} + \frac{12}{39} = \frac{12 + 12}{39} = \frac{24}{39} = \frac{8}{13}\)

13. \(-\frac{1}{21} - \frac{1}{28} = -\frac{4 + 3}{84} = -\frac{7}{84} = -\frac{1}{12}\)

14. \(-\frac{3}{29} - \frac{16}{58} = -\frac{3 + 8}{58} = -\frac{11}{58}\)

15. \(\frac{8}{40} - \frac{36}{45} = \frac{1}{5} - \frac{12}{15} = \frac{3 - 12}{15} = \frac{-9}{15} = -\frac{3}{5}\)

16. \(-\frac{8}{27} - \frac{15}{27} = -\frac{23}{27}\)

17. \(\frac{13}{30} - (-\frac{1}{1}) = \frac{13 + 30}{30} = \frac{43}{30}\)

18. \(\frac{2}{21} - \frac{1}{28} = \frac{8 - 3}{84} = \frac{5}{84}\)

19. \(5 - \frac{3}{4} = \frac{20 - 3}{4} = \frac{17}{4}\)

20. \(\frac{18}{24} - \frac{35}{-10} = \frac{3}{4} + \frac{7}{2} = \frac{3}{4} + \frac{14}{4} = \frac{17}{4}\)

Feel free to ask if you need more details on any specific problem!