If you put it after, it shouldn't be a mistake, but in this very sentence I would rather use it before the noun.
There are some adjectives that go often in front of the noun often (like "possibile", or "bella")...
And some nouns that want possessive adjectives to follw them (vado a casa mia, resta a casa tua)
Here you can find something useful regarding the topic. http://italian.about.com/library/weekly/aa072199b.htm
Okay, I usually don't complain about something like this, but I gotta ask, what exactly is a possible answer? I mean really, you either have an answer or you don't. Does this mean, 'I have an answer that might possibly be correct, but not for certain'? Or to paraphrase, 'I have a possibly correct answer?'