In answering the question, Kasich talked about efforts in Ohio to provide support for college students facing sexual harassment, such as access to confidential reporting, rape kits and the opportunity to "pursue justice after you have had some time to reflect on it all."
He also offered her advice that she should avoid parties with a lot of alcohol.
Kasich said the Ohio efforts should be extended to the rest of the country as well so that students "know exactly what the rules are" and do not feel vulnerable. He also reflected on how having two daughters affects his views on the issue.
"I have two 16-year-old daughters and I don't even like to think about it," Kasich said.
"It's sad, but it's something that I have to worry about," the student responded.
Kasich jumped in, saying he had advice.
"Well I would give you, I'd also give you one bit of advice. Don't go to parties where there's a lot of alcohol. OK? Don't do that," Kasich said as the audience applauded.
Kasich's answer to her question about how to keep campuses safe went directly to what happens after an assault, but other than avoiding parties with alcohol, he did not address how campuses can and should reduce sexual assault in the first place.
The Democratic National Committee suggested Kasich's comments were "blaming victims of sexual and domestic violence."
Kasich, however, rejected that claim when speaking to reporters after the event.
"I just said be careful where there's alcohol, and the reason why I worry about that is, it obscures the ability of people to seek justice," Kasich said. "It gets to be about he said, she said, and there's alcohol and it creates an inability to find the truth. That has nothing to do with saying that somebody who has been a victim is somehow responsible."
"As the father of two 16-year-old daughters you better believe every day I think about the threats that happen to our young women on college campuses, and make no mistake, the perpetrators have to be prosecuted to the full extent of the law," he added.
Kasich argued that he has been a leader on the issue and that his work with Ohio colleges and universities to deal with the issue of sexual assault should be an example for the country.
Kasich's Twitter account also tweeted
about sexual assault, saying: "Only one person is at fault in a sexual assault, and that's the assailant.
"That's why John Kasich has worked so hard to provide campuses with the tools they need to make sure victims have the necessary support," he added
. "Victims needs to know we're doing everything we can to have their backs, and that's happening in Ohio under John Kasich's leadership."
Among female college students, 23% said they experienced some form of unwanted sexual contact -- ranging from kissing to touching to rape, carried out by force or threat of force, or while they were incapacitated because of alcohol and drugs, according to a 2015 survey
by the Association of American Universities. Nearly 11% said the unwanted contact included penetration or oral sex.
Kasich is stumping in New York in the run-up to Tuesday's primary there, hoping a second place win in the state will help him as he trails businessman Donald Trump and Texas Sen. Ted Cruz in the delegate count.