The correct answer is A.
The sentence “He said, ‘If I had the key with me, I could give you the solution'” is in the past tense. This means that the speaker is talking about something that happened in the past. The speaker is saying that if he had the key with him at the time he was speaking, he could have given the listener the solution.
Option B is incorrect because it uses the present tense. The speaker is not saying that he could give the listener the solution, he is saying that he would give the listener the solution. This is a different meaning.
Option C is incorrect because it uses the past participle “told” instead of the past tense “said”. The speaker is not telling the listener that he would give them the solution, he is saying that he said that he would give them the solution. This is a different meaning.
Option D is incorrect because it uses the past perfect “have had” instead of the past tense “had”. The speaker is not saying that he could have given the listener the solution if he had had the key with him, he is saying that he could have given them the solution if he had had the key with him. This is a different meaning.