Rectangle \(\mathbb{A}\) is inscribed in rectangle \(\mathbb{B}\), so that each of the vertices of \(\mathbb{A}\) lies on a different side of \(\mathbb{B}\).

The length-to-width ratio for \(\mathbb{A}\) is 2:1, and the length-to-width ratio for \(\mathbb{B}\) is 3:2.

Find the ratio of the area of \(\mathbb{A}\) to the area of \(\mathbb{B}\).

If your answer is \(a: b\), where \(a\) and \(b\) are positive coprime integers, enter \(a+b\) as your answer.

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