You have done a mistake in the fourth step.
In the third step you have cancelled ln e, but mysteriously in the fourth step you have a ln e back!
Well, I was dividing one side by ln e so I could move it to the other side with the 6.Anytime you divide one side, you have to divide the other side if it has an equal sign.
So I'd get ln(x+2) = 6/ln(e)
I still don't know how to solve it properly. Can you do it?