Step 1: Write down what is given.
Volume needed, \( V = 200 \, \text{mL} = 0.2 \, \text{L} \). Target molarity, \( M = 0.15 \, \text{mol/L} \). Molar mass of NaOH, \( = 23 + 16 + 1 = 40 \, \text{g/mol} \).
Step 2: Find the moles of NaOH needed.
Molarity is moles per litre, so the moles required is molarity times volume in litres:
\[ n = M \times V = 0.15 \times 0.2 = 0.03 \, \text{mol} \]
Step 3: Convert moles to mass.
Mass equals moles times molar mass:
\[ m = n \times 40 = 0.03 \times 40 = 1.2 \, \text{g} \]
Step 4: Final Answer.
Weigh out 1.2 g of NaOH and dissolve it in water, then make the final volume up to 200 mL.
\[ \boxed{1.2 \, \text{g}} \]