To solve the given problem, we need to match each conditional sentence from List-I with the correct verb form from List-II according to the rules of English conditional sentences.

1. Type-3 Conditional: These sentences express a situation that did not happen in the past. The structure is "If + past perfect, would have + past participle".
   • (a) If you had told him the story, his heart — could be matched with (iv) would have melted. This creates the sentence "If you had told him the story, his heart would have melted," indicating an unreal past situation.
2. Type-2 Conditional: These sentences are used to express a situation that is hypothetical in the present or future. The structure is "If + past simple, would + base verb".
   • (b) If you told him the story, his heart — should be matched with (iii) would melt. This means "If you told him the story, his heart would melt," detailing a hypothetical present/future situation.
3. Type-1 Conditional: These sentences refer to a future condition that is possible or likely. The structure is "If + present simple, will + base verb".
   • (c) If you tell him the story, his heart — should be matched with (ii) will melt. This provides "If you tell him the story, his heart will melt," indicating a probable future condition.
4. Zero Conditional: These sentences are used for universal truths and facts. The structure is "If + present simple, present simple".
   • (d) If you heat ice, it — aligns with (i) melts. This results in "If you heat ice, it melts," a statement of fact or scientific principle.

Based on the above analysis, the correct matching is:

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

This matches the provided correct answer option and confirms our understanding of the conditional sentences.