> Probably a lot more than just a few months

Maybe, haven't tried so it is hard to say. I do have a background in Greek and Latin as well but I suspect those won't be of much help either nor does the fact that I speak Dutch, German, English, Swedish and French and know some rudimentary Russian get me anywhere.

Spelling and grammar in both Finnish as well as Hungarian seem to be quite regular so it would come down to learning a new dictionary, a bunch of suffixes and the rules when to use which. The dictionary would probably be the hardest since it won't be related to anything I know.