"Why do you like to drink strong coffee?"
Translation:Warum trinken Sie gern starken Kaffee?
That literally says: 'Why do you like it to drink strong coffee'. to like and mögen need an object or something that replaces the object (that, it, etc) to be complete. In German, that happens frequently: 'starken Kaffee zu trinken' is a subordinate clause. You need one of those every time you want to describe more than just an object, in this case an action. This 'it' es necessary to have a complete main clause anyway and is something like the ambassador of the sub-clause, 'es' is whatever the sub-clause later defines. That happens less often in English as far as I know, since you might say: I like talking to you – Ich mag es, mit dir zu reden. Hence, the duo's translation is also lacking a comma beteween es and starken.
I agree, but don't think this is completely true anyway. For example, I would prefer 'Ich mag es, im Schnee spazieren zugehen' or 'Ich mag es, mit dir so herumzuliegen' or my example above. I really wouldn't use gern there in any way. 'Ich gehe gern im Schnee spazieren' while doing that would feel awkward to me. For the Kaffee-example I agree though. Maybe etw. gern tun just sounds too sloppy or casual to me in some cases, where you consciously express your own liking.
(Ist der Rest ansonsten in Ordnung so?)
Hmm, for me both 'Ich gehe gern im Schnee spazieren' and 'Ich mag es, im Schnee spazieren zu gehen' sound natural. I neither feel the first one to be sloppy nor the second one to be clumsy. The coffee example is different, though. I'd very much prefer 'Ich trinke gerne starken Kaffee' over 'Ich mag es, starken Kaffee zu trinken'. But I think we all agree about that.
It is very common, you will find it everywhere, so it's important to know about it. Some more literally translated examples:
Ich weiß nicht, wie du heißt – I don't know, what your name is.
Ich habe nicht verstanden, wo das herkommt – I haven't understood, where it comes from.
Sie mag es, wie ich sie ansehe – She likes it, how I look at her.
There are many verbs in German which have to refer to something: You don't know what? You/she like/s what? You go where? Whenever the interrogative is more than just one or two words, you have this very case.
That's not correct.