How would you balance: FeCl3 + NaOH --> Fe(OH)3 + NaCl?

##FeCl_3 + 3 NaOH rArr Fe(OH)_3 + 3 NaCl##

Start with the Ferric Chloride - it's got three Chloride ions, so you're going to need 3 Chloride ions on the product side. So that's 3 NaCl. Now you've got 3 Sodium ions on the product side. They have to come from the reactant side. So make that 3 NaOH going in. Now we have one Iron going in, 3 Sodium, 3 Hydroxyl and 3 Chloride. Coming out, we have one Iron, 3 Sodium, 3 Chloride and 3 Hydroxyl.

Job done!