Here's how to determine the net ionic equation for the reaction of iron(III) chloride (FeCl₃) and potassium hydroxide (KOH):

1. Write the balanced molecular equation:

FeCl₃(aq) + 3KOH(aq) → Fe(OH)₃(s) + 3KCl(aq)

2. Write the complete ionic equation:

Fe³⁺(aq) + 3Cl⁻(aq) + 3K⁺(aq) + 3OH⁻(aq) → Fe(OH)₃(s) + 3K⁺(aq) + 3Cl⁻(aq)

3. Identify the spectator ions:

Spectator ions are ions that appear on both sides of the equation and do not participate in the reaction. In this case, the spectator ions are K⁺ and Cl⁻.

4. Write the net ionic equation:

Fe³⁺(aq) + 3OH⁻(aq) → Fe(OH)₃(s)

Therefore, the net ionic equation for the reaction of iron(III) chloride and potassium hydroxide is:

Fe³⁺(aq) + 3OH⁻(aq) → Fe(OH)₃(s)