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