\[\left( 6 - 4\frac{1}{3} \right) - \left( 1\frac{5}{7} + 6\frac{2}{7} - 7\frac{1}{2} \right) =\]
\[= 1\frac{2^{\backslash 2}}{3} - 7\frac{7}{7} + 7\frac{1^{\backslash 3}}{2} =\]
\[= 1\frac{4}{6} + 7\frac{3}{6} - 8 =\]
\[= 8\frac{7}{6} - 8 = \frac{7}{6} = 1\frac{1}{6}.\]