Translation:Why didn't she ask herself that question?
In your sentence "herself" is an intensifier: "I asked the question myself." As in, out of all the people here, I was the one who asked the question. In spoken language, "myself" would be louder or emphasized. Other examples: - I saw Brad Pitt himself! - The President himself was there. - You made that yourself.
In the sentence "I ask myself a question," the word "myself" does not intensify, but refers back to the subject (its reflexive). "I" am asking the question AND receiving the question, but in the direct object position "I" becomes "me/myself."
why is "die Frage" translated as "that question"...Duolingo has been hitherto very precise (even rigid I would say) about things like "this" versus "it", and "a" versus "the", and "a" versus "this", and versus "this" versus "the".
"Diese Frage" is not the same as "die Frage" but it's translated that way....there is another multiple choice question in this section the two different phrases words appear and the user is asked to mark the all correct versions; and there too "diese Frage" and "die Frage" are are treated as having the same meaning.