Translation:You have sixteen seconds for the answer.
"for the answer"doesn't make sense to me. Does this mean time given (for example, to a student) to come up with an answer ?
What about : "You have sixteen seconds to answer" (the question)
Your version works and I agree it is probably more common, however 'for the answer' isn't wrong and it's a direct equivalent of the Polish construction, so one can understand it more easily.
You can easily say "żeby/aby/by odpowiedzieć" in Polish, but somehow "na odpowiedź" sounds a bit better to me.
You say that 'for an answer' here isn't wrong, but it sounds very unnatural to me. Do you have an example of it being used by a native speaker? I'm genuinely curious.
While uncommon, it still sounds fine to me and I'm a native English speaker.
Once I make an error, I should get up and walk away, over and over and worse all of the time. Dupa.