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Infinitely many.

Select any point on a side and drawn a line through the centre of the rectangle to the opposite side. This line will split the rectangle in half. Since there are infinitely many points on a line and you can start with any one of them, there are infinitely many answers.

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Q: How many ways to split a 6 x 4 rectangle in half?
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If you cut a rectangle in half does it make a square?

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