a) $\frac{6}{-25} + \frac{-9}{25} = \frac{-6}{25} + \frac{9}{25} = \frac{-6 + 9}{25} = \frac{3}{25}$;

b) $\frac{1}{8} + \frac{-5}{8} = \frac{1+ (-5)}{8} = \frac{-4}{8} = \frac{-1}{2}$;

c) $\frac{11}{13} + \frac{-14}{39} = \frac{33}{39} + \frac{-14}{39} = \frac{33 + (-14)}{39} = \frac{19}{39}$;

d) $\frac{7}{14} + \frac{9}{-36} = \frac{1}{2} + \frac{-1}{4} = \frac{2}{4} + \frac{-1}{4} = \frac{2 + (-1)}{4} = \frac{1}{4}$;

e) $\frac{-12}{32} + \frac{-21}{35} = \frac{-3}{8} + \frac{-3}{5} = \frac{-15}{40} + \frac{-24}{40} = \frac{-15 + (-24)}{40} = \frac{-39}{40}$;

f) $\frac{-15}{24} + \frac{18}{-42} = \frac{-5}{8} + \frac{3}{7} = \frac{-35}{56} + \frac{24}{56} = \frac{-35 + 24}{56} = \frac{-11}{56}$.