If the sentence had been "The man really likes cheese" the translation for it would be "Manden kan rigtig godt lide ost". The "godt" is an adverb that gets added to sentences to make them more unambiguous, as in clear. For example, "Kan du lide ham?" (Do you like him?) is just as accurate as "Kan du godt lide ham?", but the latter makes it more 'personal' along with unambiguous. If you like, you can take a look at the Wikipedia article to get some more info on adverbs.
:-D that comment just made me laugh.. Funny enough that the concept exists in German, too. But it wouldn'd be used in this context here. But as "I like him" you can say: "Ich kann ich gut leiden" assumedly "jeg kan godt lide ham" which effectivly means "I can well suffer him"...
"Kunne (godt) lide" is a fixed phrase. meaning "to like". "Lide" on it's own means "to suffer", and "Manden godt lide ost" literally means "The man well suffer cheese".
The "lide" in "kunne (godt) lide" is also almost always pronounced differently to when "lide" means "to suffer". In the first example, it's usually pronounced "lee" [English phonology], whereas the second is pronounced as it's spelt [with a soft D]
Funny, immediately reminded me of 'kan het goed lijen' in Dutch, which means you can stand or suffer something, which is such an understated way of expressing 'to like' or 'to bear'. We see that as typical of Northern Dutchmen. They would also say 'Kon slechter' (could be worse) when you ask them if they are well and mean to say they are.
Really? I'm a native Swedish speaker, so as far as Swedish is concerned I think I got that covered ;) but I can swear I used 'gillar' earlier in the Danish course, and got it correct, that's why I wondered. I can of course be mistaken, but... 'gillar' would be so much easier to use than three separate words. Danish is almost easy to learn when you've known Swedish your whole life, there are so many similarities, but this just doesn't make sense to me. Although, it's a widespread opinion in Sweden that Danish doesn't make sense at all, haha.