In astronomy the term "red shift" denotes the extent to which light

Here's the version created via the use of (B).

In astronomy the term “red shift” denotes the extent to which light from a distant galaxy has shifted toward the red, or long-wave, end of the light spectrum by the rapid motion of the galaxy away from the Earth.

While the idea that light would, on its own, shift from one part of the spectrum to another may not make sense, the sentence would be basically OK, if we were to remove the prepositional phase at the end, as in:

In astronomy the term “red shift” denotes the extent to which light from a distant galaxy has shifted toward the red, or long-wave, end of the light spectrum.

However, the sentence in the question ends with "by the rapid motion of the galaxy away from the Earth." That phrase indicates that something other than the light caused the shift. It was caused by the rapid motion.

We can't change the non-underlined portion. So, we have to choose an answer choice that matches the non-underlined portion, one that makes sense in the context of the light being acted on by something else. In order to express that the subject of a sentence is acted on by something else, we need to use a passive voice verb as the main verb of that sentence.

So, in this case, we need the passive voice "has been," because the sentence is saying that the light "has been shifted ... by the rapid motion."

Notice, we can tell that we need a passive voice verb by reading the sentence and considering the meaning to be conveyed. The reason for choosing "has been" is not some arcane rule. It's that, in order for a logical meaning to be conveyed, the main verb of this sentence has to be in the passive voice.