Final answer:
The phase of the Moon when its lighted hemisphere cannot be seen from Earth is the new moon, as its illuminated side is facing away, making the Moon invisible to observers.
Step-by-step explanation:
The question is asking when the Moon's lighted hemisphere cannot be seen from Earth. When the Moon is in the new moon phase, its illuminated side is facing away from the Earth, making the Moon invisible to observers on Earth. During this phase, the Moon is located in the same part of the sky as the Sun, hence it rises and sets with the Sun, and its dark surface does not reflect sunlight towards us. Additionally, the new moon is the time when earthshine can be seen, which is the reflection of sunlight from the Earth lighting up the unilluminated part of the Moon's surface faintly.
On the contrary, other phases such as the full moon, first quarter moon, and third quarter moon are all visible to varying degrees from Earth. The full moon is fully illuminated, the first quarter shows half of the lighted hemisphere, and the third quarter also shows half, but the opposite side of the lighted hemisphere compared to the first quarter.
Therefore, the correct option in the final answer for when the Moon's lighted hemisphere cannot be seen from Earth is the new moon.