Hi Kathy,
Yup - in fact, every lunar eclipse on Earth is a solar eclipse on the moon. We see a lunar eclipse when the Earth passes between the Moon and the Sun, such that the Earth's shadow falls covers the moon. If you were standing on the Moon, you would see the Earth passing in front of the Sun and covering it for a while.
I imagine it would look very pretty as the sunlight would illuminate the Earth's atmosphere around the dark disk of the Earth.
-Christina