Part 1:
The Moon doesn't emit (give off) light itself, the 'moonlight' we see is actually the Sun's light reflected off the lunar surface. So, as the Moon orbits the Earth, the Sun lights up different parts of it, making it seem as if the Moon is changing shape.
She saw "Full Moon", "First Quarter", and "Waxing Crescent).
Part 2:
The next two phases of the moon are "New Moon" (no moon) and "Waning Crescent" (the left crescent, where the left part of the moon is seen, not the right).
PS: Sorry that this is so late, but at least other people might be able to use this :)