A person standing in the moon's what would see a particle solar eclipse?

Answer 1

In the Moon's shadow. Particularly, the "penumbra" which is the lighter partial shadow, rather than the "umbra", the darker total shadow area.

Answer 2

A person standing on the moon would see a partial solar eclipse when the Earth partially blocks the Sun's light. This is because the Earth's size in the moon's sky would be large enough to create this effect, similar to how the Moon creates a solar eclipse on Earth.