The correct answer is A. He asked her where she was going.
The sentence “He said to her, ‘Where is she going?'” is in the past tense, so it is clear that the speaker is asking a question about the past. The only option that makes sense in this context is A. He asked her where she was going.
Option B, He wanted to know where she is going, is incorrect because it uses the present tense. The speaker is not expressing a desire to know where the woman is going, he is asking her.
Option C, He wants to know where she was going, is also incorrect because it uses the present tense. The speaker is not expressing a desire to know where the woman was going, he is asking her.
Option D, He said where she was going, is incorrect because it is not a question. The speaker is not stating where the woman is going, he is asking her.