Let's say that the sides of the poster are a and b. We know that the perimeter is 2a + 2b. We know that one side is 2 times width of the other side. So we can write it all as:
72 = 2a + 2 * 2a
72 = 2a + 4a
72 = 6a / ÷ 6 (both sides)
a = 12
So one side is 12, the other one is 2 * 12 = 24 [inches]. It means that the area of the poster is 12 * 24 = 288 [square inches).
