"The children do not know the answers."
Translation:Dzieci nie znają odpowiedzi.
znać - to have information about something, to be introduced to someone
wiedzieć -to have knowlegde about something, to be aware of something.
In this context - The children do not have information about answer = > Dzieci nie znają odpowiedzi.
If you want to express that the children are not aware what the answer is you would say: Dzieci nie wiedzą, jaka jest odpowiedz - The children do not know what the aswear is.
Well , these words means almost the same , but they are not completely interchangeable , maybe you understand this with some examples , and you can use the word znać with the sentences like I know Jessica or I know this dog or I know some French words , and you can use the word wiedzieć with I do not know why or I know how to use this thing or I do not know anything
Except in this case "Dzieci nie znają odpowiedzi (Genetive) is correct, because they haven't met the answer. And the other would always be "Dzieci nie wiedzą jaka jest odpowiedź" - they don't know what the answer is or "Dzieci nie wiedzą jaką dać odpowiedź" - they don't know what answer to give (sorry, sounds terrible in English, but you know what I mean?).