What emrys said, "हमें पढ़ने की ज़रूरत है" would literally mean we need to study so he is right about that. Anytime you use an infinitive form of a verb plus chaahie it is interpreted as "should" That's why "we should study" is correct for this sentence. You probably shouldn't substitute the meaning of this sentence for "we need to study." Use the correct way that he just mentioned involving mujhe X + oblique verb/etc... ki zaroorat hai. (need to ........ etc)
Thanks. I vaguely remember the degrees of need being covered in a Rocket Hindi Module - मुझे जाना है, मुझे जाना पड़ता है , मुझे जाना चाहिए, मुह्जे जाने की ज़रुरत है - but I sometimes mix up the nuances.
It shouldn't be marked incorrect. We need to study can be translated as हमें पढ़ने की ज़रूरत है। but it shouldn't be wrong to translate it as हमें पढ़ना चाहिए।
Your translation should be marked correct. There are a lot of such sentences in here that Duo incorrectly marks wrong.