Translation:To be or not to be, that is the question.
Well, it was added by Schlegel to keep the metre, but I'd expect Duo to ask for a word-for-word translation (i.e., German to English: "this/that is the question here"; English to German: "das ist die Frage"), since the sentence doesn't exactly qualify as an idiom, in my opinion.
Of course, if the user knows the quotation and translates "das ist hier die Frage" with "that is the question", it definitely ought to be accepted. I just think Duo shouldn't demand to translate random quotations with their "literary" translation, if that's what it's doing.
I had exactly this question, and concern. Relatedly, I would sugest that Duolingo offer, and expect, direct, literal translations as much as possible, particularly for idioms. When literal translations are given/expected: a) the student learns more about german vocabulary and syntax; and b) the student has a chance to learn about how other cultures may express similar ideas differently. In this instance, Duolingo is playing a game of "telephone" with us: giving us a slightly garbled translation of the english, and asking us to recover the original. Not so helpful.
"... quoting Shakespeare is not what I am doing on Duolingo."
I understand that's not why you're doing Duolingo. Me neither. But it is what we (including you) are doing in this one exercise out of thousands of exercises. It won't hurt you or anyone to learn the most famous line from the world's greatest writer.
Only, if you hover over "das ist" it does give the choice of "this is" or "that is." I was wrong in quoting Shakespeare but not in translating this sentence, really; although, I think you are correct in saying it is usually translated, "that is." You asked why they have "hier" in the sentence and Stepintime said probably to keep the metre, but I think if someone translated it "to be or not to be that is the question here," that translation should count, too. If one does not recognize the sentence as a quote from Shakespeare, then in English, you are basically saying that you are considering (right now) the question of to be or not to be.