x+1=2(6x-18)
x+1=12x-36
x-12x=-36-1
-11x=-37
x=37/11
Verification-
x+1=2(6x-18)
LHS=x+1=(37/11) + 1 = 48/11
RHS=2(6x-18)=2[6(37/11)-18]=2(24/11)=48/11
so LHS=RHS
Hence x=37/11
As you have said before, x=4, hence by trying that
LHS=x+1=4+1=5
RHS=2(6x-18)=2(24-18)=2(6)=12
so RHS is not equal to LHS and hence x is not equal to 4.
If you know an answer, then try that answer of yours into the question in case of, an equality. Like, in this case if we would have presumed the answer as x=4 and hadn't tried it on the equation, we won't have got the answer.
So if you get an answer wrong on an equation, try solving it again until you get the answer that satisfies your equation.
Hope this helped you!