Three main-series Final Fantasy games were released for the Super Nintendo.
Those games were Final Fantasy IV, Final Fantasy V, and Final Fantasy VI. In Japan, they appeared as numbered entries IV in 1991, V in 1992, and VI in 1994. Together, they formed the series’ principal 16-bit era before Final Fantasy VII moved to the original PlayStation.
North American numbering creates the most common confusion. Final Fantasy IV was released there as Final Fantasy II, and Final Fantasy VI was released there as Final Fantasy III, because the Japanese Final Fantasy II, III, and V had not originally been localized for that market. The underlying games are still the fourth, fifth, and sixth main entries.
The count refers to main-series installments, not every Final Fantasy-branded SNES release. Spin-offs and related titles can change the total if the question is broadened, but under the standard numbered-series definition, the answer is three.