Here, the difference between A and B is one of meaning.

If we were asked to choose - without having read the rest of the sentence - whether "the extent to which light has been shifted" versus "the extent to which light shifted," we wouldn't be able to make a choice. The first is passive and the second is active, but that doesn't make the first one wrong! Active v. passive is a stylistic preference, not a grammar rule.

We have to look at the context of the rest of the sentence:

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

It's clear that the light isn't doing the shifting itself. The rapid motion of the galaxy is shifting the light. Since the light is therefore the recipient of the action, we have to use passive voice:

... the extent to which light has been shifted by the rapid motion... is correct

... the extent to which light has shifted by the rapid motion... doesn't make logical sense.

Don't use passive/active issues to narrow down answer choices until you've addressed all other grammar and meaning issues in the sentence. Sometimes it doesn't matter, and sometimes (as here) the passive voice is necessary for the meaning.

For more on the passive voice, see:
https://www.beatthegmat.com/william-sha ... tml#581346
https://www.beatthegmat.com/passive-vs- ... tml#584446
https://www.beatthegmat.com/active-vs-p ... tml#699674

No worries! But I very much appreciate your hat tip. Cheers!