Answer:
Your answer would be that the predicate is "drove slowly up the street" and the participle is "following the directions".
Explanation:
The predicate of a sentence is the part of a sentence or clause containing a verb and stating something about the subject. In the sentence above, the complete verbal predicate is "drove slowly up the steet". As the predicate is everything that is not the subject, the participial phrase is also part of the predicate. In order to identify the predicate, you should ask the following question: Who/what verb(ed)? Who drove up slowly up the street following the directions? The answer is the subject of the sentence ("the man"). As the NP "the man" is the subject, "following the directions" / "drove slowly up the street" is the predicate.
The participial phrase is "following the directions". Participle phrases always function as adjectives as they add description to a sentence. In this case, the participial phrase describes the NP " the man".
