Since this has been explained many times before and people still don't get it but I've got nothing better to do, I'll explain the whole FFVI FFIII deal.

In America:

On the NES, there was Final Fantasy I-Final Fantasy III. Later on the SNES, there was Final Fantasy: Mystic Quest(considered Final Fantasy I) and Final Fantasy II-Final Fantasy III. The NES and SNES games were completely different games, but since we American's aren't too bright, we decided to cause a lot of confusion by doing things the way we did.

In Japan:

On the Famicon, Final Fantasy I-Final Fantasy III(same as Final Fantasy I-Final Fantasy III on American NES) were released. Later, on the Super Famicon, Final Fantasy IV-Final Fantasy VI were released. Final Fantasy IV was the equivalent of the American SNES Final Fantasy II. Final Fantasy V was a game never released in America on the SNES(later released for the PS1) and Final Fantasy VI was the equivalent of the American SNES Final Fantasy III.

I'm not exactly sure what the situation was with Final Fantasy: Mystic Quest in Japan. My guess would be it was just released as a separate game outside of the series or it was never released at all. Either way, it doesn't matter.