The best revision for 'walk' is walks.
Walks is the correct option because the sentence refers to a habit, that is, to an action that someone does regularly. The mark in the sentence that allows the reader to interpret the activity (to walk to school) as a habit is the use of the adverb 'everyday'. Furthermore, the Simple Present Tense ('walks') is the one that is typically used to show habit. In addition, by using 'walks', there is subject-verb agreement since the verb has been used in the 3rd person singular. In addition, this verb and the verb of the following clause ("he lives four miles away") are in the same tense.
