Answer is: A. 1.81 mol.
Balanced chemical reaction: FeCl₂ + 2KOH → Fe(OH)₂ + 2KCl.
n(FeCl₂) = 4.15 mol; amount of iron(II) chloride.
n(KOH) = 3.62 mol; amount of potassium hydroxide, limiting reactant.
From chemical reaction: n(KOH) : n(Fe(OH)₂) = 2 : 1.
n(Fe(OH)₂) = n(KOH) ÷ 2.
n(Fe(OH)₂) = 3.62 mol ÷ 2.
n(Fe(OH)₂) = 1.81 mol; amount of iron(II) hydroxide.