the way to figure out the chemical formula is to balance charges.
Hydroxide is OH-, so it has one negative charge. iron (III) is Fe 3+, so it has 3 positive charges. thus it takes three OH- to balance one Fe3+ molecule.
so the answer is Fe(OH)3.
There are more complex iron(III) hydroxides formulas out there, but that is the one your teacher will want, and is the basic chemical formula for that base.
In order to answer more of these type of questions in the future, you will just have to memorize certain anions (hydroxide) and cations (various metals) and their charge. your teacher will tell you which ones to memorize.
