\[\boxed{\text{4.\ 208}}\]
\[\textbf{а)}\ \frac{4}{7} + \left( - \frac{6}{7} \right) = - \frac{2}{7}\]
\[\textbf{б)}\ \frac{1}{3} + \left( - \frac{2}{7} \right) = \frac{7}{21} + \left( - \frac{6}{21} \right) =\]
\[= \frac{1}{21}\]
\[\textbf{в)} - \frac{4}{9} + \frac{2}{3} = - \frac{4}{9} + \frac{6}{9} = \frac{2}{9}\]
\[\textbf{г)} - \frac{4}{7} + \frac{2}{3} = - \frac{12}{21} + \frac{14}{21} = \frac{2}{21}\]
\[\textbf{д)} - \frac{5}{12} + \frac{7}{9} = - \frac{15}{36} + \frac{28}{36} = \frac{13}{36}\ \]
\[\textbf{е)}\ \frac{8}{15} + \left( - \frac{7}{10} \right) = \frac{16}{30} + \left( - \frac{21}{30} \right) =\]
\[= - \frac{5}{30} = - \frac{1}{6}\ \]