"The girl is thinking of her dog and her cat."
Translation:Pigen tænker på sin hund og sin kat.
Part of it has to do with the fact that often times prepositions don't translate directly between different languages. Thankfully a lot of Danish prepositions have a lot in common with English ones. Then, add in verbs that require prepositions and it makes everything even messier. These are just one of those things that you have to memorize, especially when some verb+preposition combinations can completely change the meaning of the verb. Romance languages are super crazy about this.