First, we write the reaction equation:
2HCl + Ca(OH)₂ → CaCl₂ + H₂O
From this equation, we can see that two moles of HCl are required per mole of calcium hydroxide. Moreover, we know that moles, concentration and volume are related as:
Moles = molarity * liters
n = MV
2 * Moles of Ca(OH)₂ = Moles of HCl
2 * M₁ * V₁ = M₂ * V₂
2 * 0.167 * 0.0205 = 0.303 * V₂
V₂ = 0.02259 L
The volume required is 22.60 mL