Various verbs use various prepositions. Sometimes more of them and they differ in the meaning. You have to learn them individually in the same way we have to learn the English phrasal verbs one by one. "Starat se" cannot use "na" for the object.
My answer -- O Žofii se staráme -- was accepted, but it's not the answer shown at the top of the discussion. Is there a lesson that provides more information about word order in sentences? I think that would be helpful. Thanks!
Both answers are correct with the same meaning. Czech word order is relatively free. The base order is subject-verb-object. If you really want to know more about it, here is thesis which compares Czech word order and English word order https://theses.cz/id/9d4d6p?lang=en