\[\boxed{\mathbf{6.125}}\]
\[= \left( \frac{1}{14} - \frac{4}{14} \right) \cdot \left( - \frac{1}{3} \right) + 1 =\]
\[= - \frac{3}{14} \cdot \left( - \frac{1}{3} \right) + 1 = \frac{1}{14} + 1 =\]
\[= 1\frac{1}{14}\]
\[\textbf{б)}\ \left( 7 - 8\frac{4}{5} \right) \cdot 2\frac{7}{9} - 15\ :\left( \frac{1}{8} - \frac{3}{4} \right) =\]
\[= - 1\frac{4}{5} \cdot \frac{25}{9} - 15\ :\left( \frac{1}{8} - \frac{6}{8} \right) =\]
\[= - \frac{9}{5} \cdot \frac{25}{9} - 15\ :\left( - \frac{5}{8} \right) =\]
\[= - 5 + 15 \cdot \frac{8}{5} = - 5 + 24 = 19\]
\[= 101,4 + 7 \cdot \frac{3}{7} = 101,4 + 3 =\]
\[= 104,4\]