Learn Croatian: Čitam puno različitih žanrova, ali volim trilere. - I read many different genres, but I like thrillers.

The phrase različitih žanrova is in the genitive plural because it directly follows the quantity word puno (a lot of / many). In the second half of the sentence, trilere is the direct object of the verb volim (I like), which requires the standard accusative case.

The word žanr is a foreign loanword. Why does it have the -ov- part in žanrova?

Foreign loanwords usually adapt to normal Croatian grammar rules. Because žanr acts as a single-syllable masculine noun, it takes the long plural infix -ov- just like native words do. This makes its nominative plural žanrovi and its genitive plural žanrova.

Could I use mnogo instead of puno in this sentence?

Yes, you could say mnogo različitih žanrova. In everyday conversational Croatian, puno and mnogo are used almost interchangeably for "a lot" or "many," and both force the noun that follows into the genitive case.