Answer:
A. Object of the preposition
Step-by-step explanation:
Prepositional phrases are phrases that consist of the preposition, its object, and the words that modify the object.
The prepositional phrase in the given sentence is for assigning difficult projects. The object of a preposition is a noun, noun phrase, or pronoun that follows a preposition and completes its meaning. The preposition here is for, and it's followed by the gerund phrase assigning difficult projects, which completes its meaning. That makes this gerund phrase the object of the preposition for.