Simplify $\frac{2m+8}{3}-\frac{2-m}{3}$.
Both fractions have the same denominator, so we can subtract them: \[\frac{2m+8}{3}-\frac{2-m}{3}=\frac{(2m+8)-(2-m)}{3}\] Distributing the negative sign across the parentheses, we get \[\frac{2m+8-2-(-m)}{3}=\frac{2m+8-2+m}{3}=\frac{3m+6}{3}\] Notice that every number in the numerator has a common factor of 3. We can use the distributive law in reverse to get \[\frac{3m+6}{3}=\frac{3(m+2)}{3}=\frac{\cancel{3}(m+2)}{\cancel{3}}=\boxed{m+2}.\]