= Solution
The stated $x$ bounds depend on $y$, so $y$ must be held fixed while the <integral> over $x$ is performed. The intended <iterated integral> is
$$
\boxed{\int_0^1\left(\int_{2y}^2x^2y^2\,dx\right)dy.}
$$
The original PDF places the two sets of bounds beside the opposite integral signs relative to the printed $dx\,dy$. That placement cannot be read literally as a conventional nested <integral>; the dependence of the lower $x$ bound on $y$, and the explicit instruction to integrate over $x$ first, specify the intended region unambiguously.
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