"He searches for words in dictionaries."
Translation:Er sucht Wörter in Wörterbüchern.
But Duo doesnt accept "sucht nach" or it doesnt know "Worte" because Er sucht in Wörterbüchern nach Worten " was marked wrong, even if the sentence is definitly correct. And Wörter or Worte are both equal plural versuions of Wort.
But I guess the normal forum-user doesnt use Worte so often, so Duo doesnt know.
Your sentence however is not correct. „In Wörterbüchern“ can only go after whatever it is you’re searching for. Because we’re searching for words, „Er sucht nach Wörtern in Wörterbüchern“ is correct. However, „Er sucht Wörter in Wörterbüchern“ is simpler and means the same thing.
Depends on the context I guess: If you use nachschlagen, then you already know a word, and want to know how it is spelled, or what exactly it means. If you search, you might actually be looking for a word that describes the situation you want to describe (like in in thesaurus).
Admittedly, probably nachschlagen is the correct context. I'd say report it next time.