Question 105831
{{{5-2/(x-6)=10-2x/(x-6)}}} 
{{{5=10-2x/(x-6)+2/(x-6)}}} 
{{{5=highlight(12)-highlight(2x/(2x-12))}}} 

The highlighted boxes show where you made your mistakes. 
First off, in the second line, you have 10, where did the 12 come from in line 3. 
Second, when you add fractions, you need to have the same denominator. Then you can add or subtract the numerators keeping the same denominator. 
{{{A/C+B/C=(A+B)/C}}}
You added denominators. 
Let's go back to your second line.
{{{5=10-2x/(x-6)+2/(x-6)}}} 
{{{5=10+(2-2x)/(x-6)}}}
I'll leave you there. I think you can proceed from here. 
Move that 10 from the right hand side (additive inverse). 
Multiply both sides by the denominator (x-6) and then solve for x. 
Good luck. If you get stuck post another question.