We never say "не можно". Можно - нельзя
A Russian-American mother once told me that when her (bilingual) son was very young, he would sometimes get confused in Russian and try to use the non-existent* word льзя as the opposite of нельзя, instead of можно!

(* Perhaps one should say "no longer existent" -- in fact, there was a word льзя in ancient Slavic -- it was etymologically related to легко, "easy." So the original meaning of нельзя was something like "it's not easy to do," but later the meaning became "one shouldn't do it.")