Step 1 :Analyze each option:
Step 2 :A. $0.2 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{HCl}$ and $0.2 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{KCl}$: In this case, we have a strong acid (HCl) and a salt (KCl). There is no weak acid or weak base present, so this option cannot form a buffer solution.
Step 3 :B. $0.02 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{HCl}$ and $0.04 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{NH}_{3} \cdot \mathrm{H}_{2} \mathrm{O}$: In this case, we have a strong acid (HCl) and a weak base (NH3). When mixed, the HCl will react with NH3 to form NH4+ (ammonium ion), which is the conjugate acid of NH3. This option can form a buffer solution.
Step 4 :C. $0.01 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{KH}_{2} \mathrm{PO}_{4}$ and $0.2 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{Na}_{2} \mathrm{HPO}_{4}$: In this case, we have a weak acid (KH2PO4) and its conjugate base (Na2HPO4). This option can form a buffer solution.
Step 5 :D. $0.01 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{NaOH}$ and $0.02 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{HAc}$: In this case, we have a strong base (NaOH) and a weak acid (HAc, acetic acid). When mixed, the NaOH will react with HAc to form Ac- (acetate ion), which is the conjugate base of HAc. This option can form a buffer solution.
Step 6 :\(\boxed{\text{Final Answer: Option A has no buffer action.}}\)