b) Peter has many hobbies. Can you guess what they are?
Use 'what' when there are many choices. Use 'which' when there are only a few or a limited number of choices: 'Which girls do you like, blondes or brunettes?'
Thanks for your answer, Mister Micawber! The crux of the matter is that there are exactly six choices (e.g. Peter has six hobbies). So, do six choices count as "many" or as "a limited number"? Would you say that six things to choose between still go with what?
That is not a crux in language learning. You cannot play around with numbers like that. Language is not mathematics. If the limited number of choices is relatively evident, a native speaker will normally use 'which' (without thinking about it).