Translation:Please cut this paper in two.
I'm not a native speaker either, but I don't think those two words are commonly used in this situation.
「半切」being used more as a descriptive noun (half-sized, as in not full-sized) than a verb, and「真二つに」meaning "exactly into two", thus being much more specific.
For the OP, you were close, but I would usually say 「この紙を半分(hanbun)に切ってください」
Duolingo automatically generates "type what you hear" questions from the sentences in the lessons. Unfortunately, they are programmed to only accept the exact spelling of the answer from the sentence that they were generated from, because in most languages there would only be one way to "type what you hear". They are working on the problem, and and some "type what you hear" questions do accept multiple answers.
Most users recommend you use the word bank for "type what you hear" questions, or I personally just click "can't listen now" and skip them entirely.