Question 1102461
You are missing a closing parenthesis.
I assume you meant
{{{-2(x+3)-6x=2x-3(x+4)}}} .
Naturally, you started by clearing parentheses by applying the distributive property,
going from
{{{-2(x+3)-6x=2x-3(x+4)}}} to {{{-2x-6-6x=2x-3x-12}}} .
After that, you may have collected like terms on each side, to get
{{{-8x-6=-x-12}}} ,
followed by adding {{{x+6}}} to both sides of the equal sign,
to get the equivalent equation
{{{-8x-6+x+6=-x-12+x+6}}} , which simplifies to {{{-7x=-6}}}
The next step is to multiply both sides of the equal sign times {{{-1/7}}} .
Your teacher may call that divide by {{{-7}}} ).
That takes you from {{{(-7)*x=(-6)}}} to {{{(-1/7)*(-7)*x=(-1/7)*(-6)}}} ,
which simplifies to {{{1*x=6/7}}} or {{{highlight(x=6/7)}}} .
 
What you did is one if many absolutely correct ways to handle the problem.
You may not like the minus signs, but there is no reason to be afraid of negative numbers
(unless you see them in your bank account balance of the outdoor thermometer reading).