Translation:What do you like to do online?
Your dictionary is correct: '网上' translates to 'online' and is used as an adjective or even as a location, such as in the phrase '在网上' (online, on the Internet). In contrast, '上网' is a verb meaning 'to go online.'
Compare these two sentences to see the difference:
你在网上喜欢做什么？ (What do you like to do online?)
你喜欢上网做什么？ (What do you like to go online to do?)
I feel like "What do you guys like to do on the internet" should also be accepted...
I am hearing it as "zuò," which is correct. (9.21.18)
However, what may be confusing you is that the sound represented by "z" in pinyin us not the same as "z" in English. The "z" in pinyin sounds like what an English speaker might write as "dz". (Apollogies, I am not familiar with IPA, perhaps someone else can tell us what the IPA notations for these two sounds are.) I think you might just be hearing more of the "d" in the "dz" sound on this particular example.