William's life was changed forever in 1997 when Diana was killed in a car crash in Paris. He was just 15 years old at the time.
More recently, the deterioration of his relationship with Harry has seen the brothers go from being best mates to barely being on speaking terms.
William and Kate continued the discussion by asking campaigners about how best to deal with mental health issues.
The Princess of Wales said: "One of the messages we are trying to encourage is the fact that everyone has mental health, and in the same way as their physical health we have to look after, in the same way we go to the gym, we need to look after and nurture our minds as well.
"You were saying it's really important to reach out and connect with people. Some people actually, expression through music or through art or through other forms of expression, it's a really great way isn't it of experiencing mental health."
William later said: "Well as we've said at the start of this special Newsbeat [news programme], this is all about having a meaningful conversation on mental health, but it shouldn't stop here."
Kate replied: "Yep, absolutely, because talking about mental health is so important and it's definitely the first step for us all, is to keep talking, having those conversations and reaching out for help."