In which cycle do we see the full illumination of the Moon?

The correct answer is the full moon phase because this is the time when the Moon is positioned directly opposite the Sun in relation to Earth. At this point in its orbit, the entire sunlit side of the Moon is visible to observers on Earth, resulting in full illumination. This phase occurs approximately two weeks after the new moon phase.

During the new moon phase, the Moon is located between the Earth and the Sun, leading to no illuminated portion being visible from Earth. The first quarter phase shows half of the Moon illuminated, specifically the half facing the Earth, and similarly, the last quarter phase also presents half illumination but in the opposite direction. Thus, it is specifically the full moon phase where we get the complete view of the Moon's illuminated side.