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Choice D is correct. The perimeter, $P$, of a square can be found using the formula $P=4s$, where $s$ is the length of each side of the square. It's given that square X has a side length of $12$ centimeters. Substituting $12$ for $s$ in the formula for the perimeter of a square yields $P=4\left(12\right)$, or $P=48$. Therefore, the perimeter of square X is $48$ centimeters. It’s also given that the perimeter of square Y is $2$ times the perimeter of square X. Therefore, the perimeter of square Y is $2\left(48\right)$, or $96$, centimeters. Substituting $96$ for $P$ in the formula $P=4s$ gives $96=4s$. Dividing both sides of this equation by $4$ gives $24=s$. Therefore, the length of one side of square Y is $24$ centimeters.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.