first off, let's convert the mixed fractions to "improper", and then subtract.
[tex]\bf \stackrel{mixed}{8\frac{3}{7}}\implies \cfrac{8\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{59}{7}}
\\\\\\
\stackrel{mixed}{7\frac{4}{6}}\implies \cfrac{7\cdot 6+4}{6}\implies \stackrel{improper}{\cfrac{46}{6}}\implies \stackrel{simplified}{\cfrac{23}{3}}\\\\
-------------------------------\\\\
\cfrac{59}{7}~~-~~\cfrac{23}{3}\impliedby \textit{our LCD is 21}\implies \cfrac{3(59)~~-~~7(23)}{21}
\\\\\\
\cfrac{177~~-~~161}{21}\implies \cfrac{16}{21}[/tex]
