In general, how would you go about marketing a community program that is underutilized?

Don't give a general answer that is context-dependent, like, "I'd use social media," because it doesn't differentiate you from any other candidate. A wide range of answers could be acceptable, depending on what kind of program it is and why it is underutilized. If you have a specific example of doing this in a prior job, share that example.

"I would start with the characterization 'underutilized.' If the program is underutilized because it isn't spending all of its budget or because we had a target to serve 500 individuals per month and we're only serving 50, I'd first ask if our budget or targets had been set using the best data available. If the program is underutilized because we know there are people in the community who need it, but they aren't participating, then I would go to those people and find out why. Learning why a program's target audience isn't engaging is the start of marketing the program better."