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SlowZasob
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).

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