To determine which position will show three-fourths of the illuminated side of the moon from Earth, we need to analyze the positions of the Moon in relation to the Earth and the Sun.
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Position A: The moon is located at the left of the Earth. This is when the Moon is in the New Moon phase, and thus no illuminated side would be visible from Earth.
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Position B: This position is halfway between New Moon (Position A) and Third Quarter. In this position, the Moon would be in a Waxing Crescent phase, showing more than half but less than three-fourths illuminated.
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Position C: The moon is at the right of the Earth. This represents the Full Moon phase, where the entire illuminated side of the Moon is visible.
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Position D: This position is halfway between the Full Moon (Position C) and First Quarter. In this position, the moon is in the Waxing Gibbous phase, where more than half but not quite all of the illuminated side is visible.
Given this analysis, three-fourths of the illuminated side of the moon would be most visible in Position D, when it is in the Waxing Gibbous phase. Thus, the answer is:
D