This question examines the understanding of grammatical parts of speech in a sentence. The correct answer is 'D. Gerund' because 'following' is used as a gerund to show an action that is happening at the same time as the main verb 'walked'. 'A. Noun', 'B. Verb', and 'C. Adjective' are incorrect as they do not describe the function of 'following' in this context.