What is the chemical formula for manganese (III) sulfite

Manganese(III) has a +3 charge

sulfite has a -2 charge

Two manganese(III) ions and three sulfites are balanced

Mn2(SO3)3 where all the numbers are subscripts

Manganese (III): Mn 3+
Sulfite: SO3 2-

Their charges cannot be directly balanced, therefore you have to find their least common multiple, which is "6" in this case.

3x2 = 6
2x3 = 6

So for Mn (III), you multiply by 2, and for SO3, you multiply by 3 because it has a -2 charge.

Mn2(SO3)3 <- don't forget parentheses for polyatomic ions!

MnSO3