Kolik cizích jazyků znáš? = 'How many foreign languages do you know (about/of)?' (= You have the knowledge of them, you are aware of their existence.)
Kolik cizích jazyků umíš? = 'How many foreign languages can you speak?' ( = You have the ability to use them.)
Though, if you asked me the first question, I'd immediately assume you mean the second one (it's a bit of a strange question) so the meaning is kinda flexible.
Suppose you can read and perhaps also write a language (thanks to DuoLingo!), but can't really speak or hear it well. You could still use "umět", right? So I see three different situations:
1. znát - have knowledge of
2. umět - have (some) skill/capability at
3. mluvit - literally speak
(For 3, I might say How many DO you speak rather than how many CAN you speak.)
Things get complicated because, unlike in English, in Czech (and also German, for example), you can literally say "I can French, I can Italian", etc. (umět), whereas in English you have to provide a verb after the "can". People usually provide "speak" as the second verb, but that is not always really accurate.