Option A – In the given sentence, the preposition “to” indicates the movement of the subject “I” towards something – in this case, Delhi and Agra. “With” on the other hand, is typically used when two or more things/persons act together or are involved. Therefore, “with my parents” would mean that both the subject “I” and his/her “parents” performed the same movement/action. (that is, travelling to Delhi and Agra). This sentence is correct.
Option B – Option B changes the meaning of the sentence. Using the prepositions in this order would indicate the movement of both the subject “I” and the places “Delhi and Agra” towards the subject’s parents, which is semantically incorrect.
Option C – “At” is typically a preposition that indicates time and even when it's used to indicate a place, it refers to a specific place. Delhi and Agra are not names of specific places and the verb “went” indicates movement of the subject “I” towards a destination. Thus, it would be incorrect to use Option C in the given sentence.
Option D – While “to” is correct (as mentioned above), using the preposition “by” before “my parents” turns the subject's parents into a place.