I am sorry that I _____ before I _____ the explanation.
1) had stopped – finished
2) stopped – had finished
I agree with the answer key. Given those two choices, (2) is the only option that works. It would also be OK to use the simple past in both clauses:
3) I am sorry that I stopped before I finished the explanation.
Additionally, we could reduce the "before"-clause such that it would have a nonfinite verb phrase with an implied subject:
4) I am sorry that I stopped before finishing the explanation.
If we're using a finite "before"-clause, though, the past perfect works particularly nicely here because it suggests that the explanation was not completed.
2) I am sorry that I stopped before I had finished the explanation.
The reason (1) doesn't really work is that it indicates that the speaker is apologizing for stopping and then finishing the explanation.