Solid iron(iii) hydroxide decomposes to produce iron(iii) oxide and water vapor. if 0.75 l of water vapor is produced at stp, how many grams of iron(iii) hydroxide were used?

The reaction is 2Fe(OH)3 --> Fe2O3 + 3H2O, so the mole ratio of iron (III) hydroxide to water is 2 to 3, or 0.667. That means you need 0.667 moles of iron(III) hydroxide for every mole of water that forms. 

You are missing some info. You need the volume of the water vapor. At STP, 1 Liter of gas contains 22.4 moles, so you can find the moles of water vapor once you know the volume of the water vapor in Liters. 

Then, mulitply moles of water by 0.667 to find moles of iron (III) hydroxide used. Finally, multiply by the molar mass of iron (III) hydroxide to find the mass in grams.