The correct answer is D. I asked her if she knew how to dance.
The sentence “I said to her, ‘Do you know how to dance?'” is a direct question. Direct questions are used to ask for information. In this case, the speaker is asking the listener if they know how to dance.
The answer choices A, B, and C are all incorrect because they do not represent the meaning of the sentence. Option A, “I asked her if she does know dancing,” is incorrect because the speaker is not asking if the listener does know dancing, but if they know how to dance. Option B, “I asked her if she had known how to dance,” is incorrect because the speaker is not asking if the listener had known how to dance in the past, but if they know how to dance now. Option C, “I asked her if she was known how to dance,” is incorrect because the speaker is not asking if the listener is known how to dance, but if they know how to dance.
Therefore, the correct answer is D. I asked her if she knew how to dance.