What does a red shift indicate about a galaxy?
a. it is moving toward earth.
b. it is moving very fast.
c. it is slowing down.
d. it is moving away from earth.

The only cause we know of that could shift the spectrum of a source toward longer wavelengths isthe source moving away from us. That's how we interpret the red shift when we see it, and that's where the whole idea of the expanding universe comes from. But ... just like gravity and the Earth going around the sun ... it can't be proved, so it's "only a theory".