The sentence is a story. There is a dog. There is a cat. But, the particle 의 is attached at end of the word for dog, not cat.
"개의" = "dog and".
Sometimes word order matters. This word unit of the sentence is an example. Here, the two languages have a grammar rule that keeps the same word sequence across translations.
Within sentences, some word units or phrases can be moved around, to the beginning or elsewhere. We do that to give our listener clues Example:
I never do my homeworøylat home.
In the morning, at home, I never d
I'm not sure I see much value in such sentences--sentences that have never been uttered by a Korean since the beginning of time! If anyone is interested in discussing the pros and cons of the Duolingo Korean app, please join my Facebook page: https://www.facebook.com/groups/585229261922235/
If you want to memorize useful phrases, I highly recommend buying an old-fashioned phrasebook.
If you want to pick up grammar by knowing how to rearrange words into original sentences, then stick with Duolingo (or hire a professional language teacher).
When you can understand Duolingo's quirky sentences like this first time you see them you know it's because you now know enough grammar. Because they're grammatical but not "sensible" you can only know them by knowing the grammar, and not by memorizing them without understanding.