Hi Kathy!

Sure they can! When a total lunar eclipse happens here on Earth, the Moon has passed directly behind the Earth into the darkest part of the Earth's shadow, which is called the umbra, so the Earth is blocking the sunlight that normally would illuminate the full Moon. From the point of view of a lunar explorer, the Earth would be blocking out the Sun, so that if you were on the Moon when a total lunar eclipse was happening on the Earth, you would see a solar eclipse on the Moon instead!

Kris