The correct option is
A to buy
Answer : C
In the sentence, "I" is the subject, "went" is the verb, "shoes" is the direct object, and "shop" is the indirect object.
The sentence therefore has the structure [Subject] + [Verb] + [Object]. It is in active voice.
By grammar rules, the infinitive form to the verb is used in an active voice sentence following the main verb.
A verb is converted to it's infinitive form by adding "to" before the base form of the verb.
Therefore, the infinitive form of "buy" is "to buy".
And so the suitable option here is "to buy".
Thus, the correct complete sentence is:
I went to the shop TO BUY some shoes.