What fraction of the moon can be seen from the moon when the moon is at its third quarter phase?

Answer 1

Half of it, the same as always. Half of the visible side of the Moon will be brightly lit by the Sun, and the other half is often dimly visible by reflected earthshine, sunlight that is reflected from the Earth and then shines down on the night side of the Moon.

Answer 2

At the third quarter phase, half of the moon is illuminated by the sun, but the side facing Earth appears as a crescent. So, from the moon, you would be able to see half of the moon illuminated, which would appear as a half-moon shape.