"The professor had wanted to know why we had not done the exercises."
Translation:Il professore voleva sapere perché non avevamo fatto gli esercizi.
Hi Chris - my explanation is that the Past Perfect tense signifies events that happened before Imperfect tense events. In this case, " we had not done the exercise" takes place before "the professor had wanted to know." I don't know if you agree, but "The professor (eliminating had) wanted to know why we had not done the exercises" is a more likely english sentence and illustrates better the difference between imperfect and past perfect. (As always, my explanations are long-winded and might not make any sense)
I think the better English translation of "La professoressa voleva sapere perché non avevamo fatto gli esercizi." is "The professor wanted to know why we had not done the exercises."
In both the Italian and the English, the pluperfect (or past perfect) is used only in the second clause; the first clause is a simple imperfect + infinitive: She wanted to know/voleva sapere.