I assume you meant x + 6 as a numerator and x - 8 as a numerator although that is not what the equation you wrote means.
[tex] \dfrac{x + 6}{2} - \dfrac{x - 8}{3} = 5 [/tex]
[tex] \dfrac{x + 6}{2} \times \dfrac{3}{3} - \dfrac{x - 8}{3} \times \dfrac{2}{2} = 5 [/tex]
[tex] \dfrac{3(x + 6)}{6} - \dfrac{2(x - 8)}{6} = 5 [/tex]
[tex] \dfrac{3x + 18}{6} - \dfrac{2x - 16}{6} = 5 [/tex]
[tex] \dfrac{3x + 18 - 2x + 16}{6} = 5 [/tex]
[tex] \dfrac{x + 34}{6} = 5 [/tex]
[tex] \dfrac{x + 34}{6} \times 6 = 5 \times 6[/tex]
[tex] x + 34 = 30 [/tex]
[tex] x = -4 [/tex]
