Learn Danish: Kan du lide at danse? — Nej, det kan jeg ikke. - Do you like to dance?

Yes, kan normally means "can". However, Danish doesn't have a single verb that translates directly to "like". Instead, it uses the fixed phrase at kunne lide (which literally means "to be able to endure"). Because of this, kan du lide is the standard Danish way of asking "do you like".

Why is there an at before danse?

at is used here exactly like the "to" in "to dance". It is placed before the basic, dictionary form of a verb (the infinitive). A helpful tip for listening: in everyday spoken Danish, this at is usually pronounced like a short "å" sound rather than how it is spelled.

Why isn't there a word for "do" in the Danish question or answer?

Danish doesn't use a "do" helper word to ask questions or make negative sentences. Where English says "Do you like?", Danish simply swaps the verb and subject to ask "Can you like?" (Kan du lide?). For the answer, instead of "I do not", Danish just uses the negative word ikke.

In the reply, why do we need the word det?

In English, you can answer simply with "No, I do not." But in Danish short answers, you usually need a placeholder word to refer back to the activity you were just asked about. Here, det acts as "it" or "that" (referring to dancing). You are essentially saying "No, that I cannot [like]."

Why is the word order in the reply instead of ?