1. I got the same answer as yours:
P = 2 (15 + w)
2. I also got the same as yours:
P = 2 (15 + w) ≤46
3. To solve for the width we have to leave the w to the left side alone like this:
15 + w ≤ 46/2
W ≤ 23-15
W ≤ 8 feet
4. The width of the banner is less than or equal to 8 feet.