"Vil du besvare brevet?"
Translation:Do you want to answer the letter?
To 'Besvare brevet' is to act on behalf of what the letter (brev) contains of infomation. To 'Svare brevet' is to talk directly to the letter (which does not make any sense unless you are Harry Potter). The same goes for calls 'besvar mit opkald' (answer my call) and 'besvar spørgsmålene i quizzen' (answer the questions in the quiz). You direct your answers to another person/reader/receiver/thing than the subject in the first sentence, i.e. you react on it.
On the other hand, you can't say "besvar mig!" but only "svar mig!" (answer me!), as you should direct you answer to the person in question.
I think, it's the same thing as with German "antworten" and "beantworten". So if you use "svare" you have to use a preposition "på" (Vil du svare på brevet?). If you use "besvare", the preposition isn't necessary. But I'm not sure, that's the way it works in German.
As far as I can tell, "svare" would mean to answer a question, whereas "besvare" is closer to reply.
@PatrykPias1 That is correct. @virapis Not quite, the word "reply" can in Danish easily be "svare", for example in "Please reply" = "Svar venligst". The words do not have direct English counterparts, but the explanation from @Hamburg is good and makes it clear that "svare" is to the person/object, while "besvare" is to the content".
Could this also be translated as "Will you answer my letter?" Does the translation depend on context or am I missing something?
Yes, "Will you answer the letter" can also be a translation. The meaning is slightly different since now it is a future tense (asking if you WILL do it rather than if you WANT TO do it), which in this case is no different in the Danish sentence.
"brev" = "letter" and "post" = "mail"
In Danish you can say "Du har fået post" = "You've got mail" but you can't really refer to the mail as something to answer. "Answer the mail" works in English, but "Svar på posten" is an odd Danish construction. It could work if you really stretch it in the case that you have much different kind of mail (letters, postcards etc.), but if you only talk about letters or only about one letter, you will use the word "brev" or "brevene".