Dank

[wet charm]

What comes after "Dank", Dativ oder Gen?

[echo cedar]

You'll generally see a lot of prepositions in German that are acceptable both in genitive and in dative. Most (if not all) of these originated with genitive, and the dative usage is becoming more prominent as genitive is dying off.

The best way to tell is to look up the preposition in a German -> German dictionary. Even if you don't understand the whole thing, they'll tell you the grammar of it.

So for example for mit https://www.dwds.de/wb/mit you'll find that it's strictly a dative preposition. But for dank https://www.dwds.de/wb/dank it'll tell you that both genitive and dative are okay, and it'll give you usage examples for both.

[dull pewter]

der Dank (thanks as a noun, as in "you'll get no thanks for that) vs. dank (preposition, thanks to) ;)

[tepid walrus]

dank des ... -> Genitive (thanks to the ...)

[wet charm]

Thanks I'm taking notes