You see the right half of the moon illuminated during a third quarter moon.

Here's why:

* Moon Phases: The moon doesn't produce its own light. We see it because it reflects sunlight. As the moon orbits the Earth, the angle at which the sunlight hits the moon changes, creating different phases.

* Third Quarter: In the third quarter phase, the moon is about 90 degrees away from the sun in the sky. This means only half of the moon is illuminated from our perspective on Earth.

* Right Half: Since the sun is behind the moon, the right half of the moon is facing the sun and therefore illuminated.

So, when you see a third quarter moon, it will look like a half-moon with the illuminated side on the right.