Answer:
B. Inspire community involvement
Step-by-step explanation:
As you can read in the sentence, we are talking about what the public libraries do, and the best way to express what something does is to say:
Public libraries inspire community involvement. if the sentence was talking of what the public libraries are doing, we should use D. Inspiring community involvement, encouaging learning and providing low cost resources, but that not the tense in which the sentece is talking, so the answer would be B.