The correct option is B Do
Option A is correct as the sentence needs an auxiliary or helping verb and not the main verb to complete its meaning. The verb 'do' here means perform an activity of one's choice. Hence, it's use in the sentence brings out the desired meaning that the speaker's parents allowed him/her to perform the activity of his or her choice, when he or she was young. Option B is not correct as the sentence does not need an infinitive. Option C cannot be used as the sentence does not need a gerund. Option D cannot be used as it would render the sentence incorrect grammatically.