The correct option is
B used to
Option B: 'Used to' is a semi-modal verb that expresses a discontinued habit. It completes the given sentence in meaning, stating that the person 'used to play basketball' while he was in high school. Hence option B is correct.
Option A: 'Use to' is generally used in interrogative constructions with the verb 'did': 'did she use to play with us?'
The form 'used to' is most widely used when referring to any past habit, as opposed to 'use to'.
Hence option A is incorrect.
Option C: 'Like' in 'like to' is a simple present verb. It indicates a present habit. Also, 'like' is a verb in the second person narrative (or the third person plural). The verb here 'he' is in third person singular. Hence this verb form isn't suitable and option C is incorrect.
Option D: 'Always' refers to a daily habit. It should be followed by the verb 'plays' as opposed to the verb 'play' in the sentence.
(Since the sentence refers to a past habit, the form 'play' is used.)
Hence option D is incorrect.