I think you may have messed up on your signs a tad because you added 18 to both sides instead of subtracting it.
18-3w=4
+3w +3w
-4 -4
You can add over the 3w to make it positive and subtract the four from the 18 like so
18-4=3w
18-4 simplifies to 14
so 14=3w
now divide by 3
14/3=w
and that's your answer.
Be sure to plug in the values you find back into the problem to see if both sides end up equivalent.
4=18-3w
18 - 3w=4
+18 +18
-3w=22
7 1/3
2 answers
Adding 3w-4 on both sides
3w-4+4=18-3w+3w-4
3w=14
dividing both sides by 3
3w/3=14/3
w=14/3
3w-4+4=18-3w+3w-4
3w=14
dividing both sides by 3
3w/3=14/3
w=14/3