What is the solution to the equation 2/3x+1=1/6x-7?

As it is, in accordance with the priorities of the operators (or the PEMDAS rule) the equation without parentheses mean
(2/3)x+1=(1/6)x-7
I do not suppose you mean the above, since the solution is relatively trivial.

I suppose you actually mean
2/(3x+1)=1/(6x-7)
in which case you would cross-multiply:
2(6x-7)=(3x-1)
and expand/distribute
12x-14=3x-1
isolate x and solve
12x-3x=-1+14
9x=13
x=13/9
If you mean the first form of equation without parentheses, my apologies.

6/9 i need more characters in my answer