I believe that was going to be "This cannot be possible!"? Anyway, as immery stated in the comments above, the literal translation rule. I believe we need you to use the word "impossible" and not "not possible". Frankly, "impossible" sounds stronger to me.
"To nie może być możliwe" sounds strange mostly because of the repetition of może-, I'd say "To nie może być prawda!" which is kind of a fixed phrase (This cannot be truth = This cannot be true)