Translation:When do we begin to study?
Verbals are verbs that are used as other parts of speech. For examples of verbals, read my comment to Clari64.
When verbs follow each other in a Spanish sentence but are used as different parts of speech, I suspect that perhaps the "a" is a clitic signifying that the first verb (in this case, "empezamos," the predicate verb) is followed by a verbal acting as another part of speech. In this case, the infinitive verb "estudiar" is acting as an adverb substitute that is narrowing the action of the predicate to "starting to study," as opposed to something like "starting to sing."
Yes I agree also. I tried, 'When are we going to start studying' but i realise that was a bit too far off what was needed.
Au contraire! Your alternate interpretation, like that of Colette984040, should be reported as correct colloquial translations. Quite simply, depending on the nuance you want to convey, it is your choice whether to translate Spanish simple tense to English simple tense or English present progressive tense. Likewise, "estudiar" can be translated either into the infinitive "to study" or into the English gerund "studying," either of which can be used as the direct object of "empeza/start/begin."
It's not often I disagree with the Jersey Shore, Linda, but I think Clari's initial doubt was correct. Everything you say above is sound but you do not address Clari's "going to start" which I think is adding more than the original sentence suggests.
My answer was "When will we start studying?" but the "correct" answer given was "When did we start studying?" I'm pretty sure my answer is correct and Duolingo's is wrong.
If those are the exact words you used, Eun, then you are wrong. To be a proper English sentence, it would have to be either "When do we start" or "When are we starting.". "When are we start" is not proper English under any circumstances.