Fe(OH)₂ is solid which partially dissociates into its ions in water. It produces Fe²⁺ and OH⁻ ions by dissociation.
The equation for the reaction is;
Fe(OH)₂(s) ⇄ Fe²⁺(aq) + OH⁻(aq)
to balance the equation, both side should have same number of atoms in each element.
Left hand side has 1 Fe, 2 O and 2 H atoms while right hand side has 1Fe, 1 O, 1H. hence the equation is unbalanced. to balance that, to the right hand side 2 should be added before the OH⁻ ion. Then the balanced equation is;
Fe(OH)₂(s) ⇄ Fe²⁺(aq) + 2OH⁻(aq)