Question 84879
Your initial set-up is quite ok!
{{{x/6 + 2x = x-8}}} Simplify by multiplying through by 6.
{{{x + 12x = 6x-48}}} Combine like-terms.
{{{13x = 6x-48}}} Subtract 6x from both sides.
{{{7x = -48}}} Finally, divide both sides by 7.
{{{x = -48/7}}} 

Check: Substitute {{{x = -48/7}}}
{{{(-48/7)/6 + 2(-48/7) = (-48/7)-8}}} Simplify.
{{{-8/7 - 96/7 = -48/7 - 56/7}}}
{{{-104/7 = -104/7}}} It checks!