Concept:In reported speech, the tense and modal verbs shift to match the past tense of the reporting verb.
Explanation:The reporting verb is
asked, which is in the past tense.
The original offer was "Would you like to go...?"
When reporting a past offer, the modal
would is retained to express willingness.
The speaker is saying "I said I would [like to go]."
Options A, B, and D do not fit the reported structure or the intended meaning.
Answer:C. would