Translation:I don't think she entered without the husband.
Why wouldn't it be suo marito rather than il marito if it was hers? It's clothing and body parts where Italian drops the possessive pronoun and just uses the definite article.
It is hard getting used to article and possessive differences between English and Italian. I still occasionally forget to add the definite article to the possessive (or to leave it off for family members).
il suo tavolo
il suo fratello
Family members usually drop the definite article when referring to each other, but in this case it's uncertain to whom the husband belongs!! I assumed that he belonged to the 'she' in the sentence, and in those circumstances the thing owned or a part of usually drops the possessive. Well, both possibilities are accepted now I believe or this particular translation, either 'her husband' or 'the husband'. Tricky navigating the differences between languages ....
"I don't think she has entered without her husband" was the answer given. But this doesn't sound right to me. I think we are more likely to say "I don't think she will have gone in without her husband". Although I don't know whether DL accepts it or not.
The subjunctive is being used here where we are expressing doubt, and we have various ways to that in English.
Why can it not be "I do not think that you entered without your husband"? 'Sia' is ambiguous as to its subject, right? So the sentence could be "I do not think that I entered...", "I do not think that you entered...", "I do not think that she entered..." Plus, it could have been used in a formal setting, so even if the sentence forced it to be in the third person, it could still be translated as you.
Duo usually/often does not include the "formal you" option in its list of correct answers for some reason, but will sometimes do so if reported. So it is safer just not to use it to avoid the frustration.
As a footnote, it could not have been "I do not think that I entered" since where the subject in the main clause and the subordinate clause are the same the subjunctive is not used. The di + infinitive construction is used instead, as in non penso di essere entrato....