\[3\frac{7^{\backslash 3}}{8} - 6\frac{5^{\backslash 4}}{6} = 3\frac{21}{24} - 6\frac{20}{24} =\]
\[= - \left( 5\frac{44}{24} - 3\frac{21}{24} \right) = - 2\frac{23}{24}.\]