"Eles me mostram sua casa."
It doen't differ. But your translation is better than Duolingo's. Actually, it is more natural to say "Eles me mostram a casa deles" if you want to say "They show me their house".
It should probably also accept, "They show me his house" since that's a perfectly natural thing to say. It has multiple translations, the correct one could only be inferred by context which is lacking in this sentence.