"Then, she must have been at the house."
Translation:Entonces, ella debe de haber estado en casa.
"Deber de" is used to express probability. In this sentence, another translation would be something like "it is very likely that she was at home".
"Deber" (without "de") is used to show obligation. She had to have been at home (to receive a package, to let the repairman in, to make sure no rowdy kids hang out in the backyard, etc).
Take a look at this article: https://spanish.yabla.com/lesson-Deber--Deber-De-%2B-Infinitive-197
These exercises with "deber" are making me realize that I don't thoroughly understand the proper (prescriptive) use of "must" in English, as opposed to the verbs "have to" or "should." This page about English use and conjugation (or not) or "must" shows why translating from "deber" to English and vice versa can be a little tricky -- or at least irregular. https://www.englishpage.com/modals/must.html
Cut and pasted: Is it "en casa" or "en la casa"? | SpanishDict Answers www.spanishdict.com › Q&A › Vocabulary & Grammar According to one grammar book, it says it could be either; but "en la casa" is more common in Latin America. In another book, it says that it is always "en casa," unless "casa" is modified by a phrase to make it stand out, as in "en la casa blanca."...
I wondered this myself, and it was my first guess for this exercise. After reading Writchie4's comment about how this is most likely a sentence about probability, I now see that the verb "must" is being used in the present tense. Therefore (as I understand it), we can conjugate "deber" in the present tense.
In effect, something like, "Then [given the evidence, we conclude that] she must [present tense] have been [reference to past state, but not an active conjugated verb] in the house."
That's my stab at it, anyway.