- A: \( ^{222}_{86}Rn \to ^{218}_{84}Po \) undergoes alpha decay, emitting a \( \alpha \)-particle, so the correct match is \( \text{A-II} \).
- B: \( ^{214}_{83}Bi \to ^{214}_{84}Po \) undergoes beta decay, emitting a \( \beta \)-particle, so the correct match is \( \text{B-I} \).
- C: \( ^{234}_{90}Th \to ^{234}_{92}U \) undergoes alpha decay, emitting a \( \alpha \)-particle, so the correct match is \( \text{C-IV} \).
- D: \( ^{22}_{11}Na \to ^{22}_{10}Na \) undergoes beta decay, emitting a \( \beta \)-particle, so the correct match is \( \text{D-III} \).
Thus, the correct matching is: A-II, B-I, C-IV, D-III.