Molarity is defined as the number of moles of solute dissolved per litre of solution. The formula is (M = n/V), where (n) is the number of moles and (V) is the volume in litres. Rearranging: (n = M \times V = 0.4 , \text{mol/L} \times 0.500 , \text{L} = 0.2 , \text{mol}). Mass of NaOH required (= n \times M_r = 0.2 \times 40 = 8 , \text{g}). Option 4 g corresponds to only 0.1 mol, which would give a molarity of 0.2 M in 500 mL, not 0.4 M. Option 16 g corresponds to 0.4 mol, yielding 0.8 M in 500 mL. Option 20 g corresponds to 0.5 mol, giving 1.0 M in 500 mL. This is a direct application of the NCERT definition of molarity and solution preparation, a standard JEE and laboratory context. Plausibility check: 8 g of NaOH in 0.5 L gives (0.2 , \text{mol}/0.5 , \text{L} = 0.4 , \text{M}), confirming the answer is correct.