Final answer:
On May 17, the Moon would be in its third quarter phase, approximately a week after the full moon on May 6.
Step-by-step explanation:
If the Moon reaches the full phase on May 6, then on May 17, it will be approximately at the third quarter phase. The Moon goes through its cycle from new moon to full moon and back to new moon in about 29.5 days.
After the full moon, the Moon shows its waning phases, which means it appears to get smaller each night.
About a week after the full moon, the Moon is at the third quarter phase. During this time, half of the Moon's illuminated side is visible, and it rises around midnight and sets around noon.
The lunar phases occur due to the changing positions of the Earth, Moon, and Sun in relation to each other. As the Moon orbits Earth, different portions of its illuminated side become visible from Earth's perspective, creating the various phases we observe throughout the month.