In a week that has seen the couple's schedule full of royal engagements, they have returned to Scotland - where they first met at St Andrew's University in 2001.
Taking a break from hosting Chinese President Xi Jinping and his wife Peng Liyuan at a state banquet at Buckingham Palace, the royal pair are making a trip that will focus on highlighting mental health issues affecting young people.
Kate, 33, who is known as The Countess Of Strathearn in Scotland, told crowds this morning that she hates when Prince William rides his motorbike - he famously was seen riding it the night before the royal wedding in 2011.
Asked by a well-wisher if her husband still rode the Ducati bike, she replied; 'He's still riding it. It always fills me with horror when he goes out on it... I'm terrified.'
And as most mothers would agree, Kate said she will try her hardest to keep her eldest son George off the bike, which can reach speeds of 190mph.
The mother-of-two, who wore a blue wool coat by the Scottish designer Christopher Kane, started the day by meeting a crowd of children during a public walkabout at a family fun day hosted in the Dundee Reparatory Theatre.
Later the parents will meet young people who are dealing with mental health challenges, take part in an anti-bullying workshop and hold private meetings with leaders in the young mental health sector.
This is a cause that has been made a priority in the charity work of William and Kate, and younger brother Prince Harry.
One of the workshops they will be attending aims to end mental health discrimination in Scotland.
At the beginning of this month, William also attended an anti-bulling workshop in London, as part of his work with The Diana Award, the charity established in his mother's name.
At the event he spoke about how becoming a parent himself had helped him to understand the impact of grief as 'the worst experience that any child or parent can endure'.
The pair's day will finish with a visit to Abertay University where the Duke and Duchess will meet students in the BAFTA young designer program.