Answer
n=3
Work Step by Step
$\frac{n+1}{8}-\frac{2-n}{3}=\frac{5}{6}$
Lowest Common Denominator (LCD) is 24
$(\frac{3}{3}\times\frac{n+1}{8})-(\frac{8}{8}\times\frac{2-n}{3})=(\frac{4}{4}\times\frac{5}{6})$
Drop LCD
3n+3-16+8n=20
11n=20-3+16
11n=33
n=3