In a right pyramid with a square base, a plane cuts the pyramid parallel to the base, forming a smaller square cross-section. The side length of the base of the pyramid is 10 meters, and the side length of the smaller square cross-section is 6 meters. If the height of the pyramid is 12 meters, at what height from the base is the smaller square cross-section? Express your answer in meters. Let's think step by step and output the final answer within \boxed{}.
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