I read this equation as 3/(x-3) = 6/8. If that is how you meant it to be, the answer to the question ends up being x = 7. Here's how to get there.
First, multiply both sides by (x-3). That gets you
3 = .75 (x-3)
Multiply out the right side of the equation.
3 = .75x - 2.25
Add 2.25 to both sides and you get
5.25 = .75x
So then you need to divide both sides by .75 to get one side to just be x.
When you do that, you get
x = 7