Translation:Can I look at my textbook?
In this sentence it is heavily implied to be your own textbook. Spend a few years (or even just 45 minutes) in a Japanese classroom and you'll see what I mean. But yes, it could also just be translated as "the textbook." Not the best or better translation though in most cases, keep in mind.
Sentence that needs to be translated has nothing to go with textbook, in terms of specifying anything about it. The word blocks for translation contain both "my" and "a". I think that without any context, and especially considering Duo's own inconsistencies (not to mention certain utter nonsenses), both of those should be accepted as correct answers.