the cheap answer is, you can just multiply both sides by 6, that way you get rid of the denominator.
[tex]\bf 15-\cfrac{1}{6}n=\cfrac{1}{6}n-1\impliedby \times 6
\\\\\\
\boxed{6}\left( 15-\cfrac{1}{6}n \right)=\boxed{6}\left( \cfrac{1}{6}n-1 \right)
\\\\\\
\boxed{6}\cdot 15-\boxed{6}\cdot \cfrac{1}{6}n=\boxed{6}\cdot \cfrac{1}{6}n-\boxed{6}\cdot 1\implies 90-n=n-6
\\\\\\
90+6=n+n\implies 96=2n\implies \cfrac{96}{2}=n\implies 48=n
[/tex]
