The correct answer is C: enjoyed.
The sentence is in simple past tense ("walked"), so the second verb must also be in simple past tense — "enjoyed."
When two actions happen in the past in the same sentence, both verbs must be in simple past tense. "Did enjoyed" (D) is grammatically incorrect — "did" is already a past marker, so the main verb stays in base form. "Will enjoy" (B) is future tense. "To enjoying" (A) is not a valid verb form here.