The correct answer to this open question is the following.
You forgot to include the options of the question, however, we can answer the following.
A correct analysis of the sentence would be "The prepositional phrase “on the park bench” acts as adjectival phrase."
In this case, the prepositional phrase is going to modify the non that is " the kindly old man." The preposition in the sentence is "on the bench," the place where the old man is seated while feeding the pigeons with breadcrumbs.