The Duke of Cambridge has said it took him "an awfully long time" to figure out what he wanted to be in life.
William told young people in Cornwall that it is "totally cool" for them to be unsure about what they want, while the Duchess admitted that she found it "difficult" herself.
The future king and his wife were discussing careers with young people at a youth centre.
He and Kate spoke to teenagers, volunteers and staff at Zebs, a youth centre in Truro, which is operated by Young People Cornwall.
During their visit the couple viewed facilities at Zebs, including a music recording studio, cafe and community area.
They watched teenagers take part in an activity in which Harry Potter author JK Rowling's circumstances before she wrote the best-selling books were discussed.
Kate then asked the group: "Do any of you know what you would love to be? Do you have some aspirations?"
William cut in: "It is totally cool not to have that, by the way. It took me an awfully long time to work out what I wanted to be."
The Duchess added: "It is so difficult because there's so much out there. It is hard, isn't it, to pinpoint one thing? William is right. I found it difficult as well."
Earlier, William was given a kiss and a hug by a tactile admirer when he arrived in Cornwall - and then joked with Kate to watch out for the well-wisher.
William was greeted with open arms by Linda Moore, who had rushed to Truro town centre when she heard that the couple were touring the county.
After visiting Truro Cathedral, where they signed a slate to publicly back the building's multimillion-pound roof appeal, the royal couple went on a walkabout to meet the hundreds of well-wishers who were standing five deep behind crash barriers.
Mrs Moore, 62, a retired teaching assistant from Truro, said she told the Duke he looked like his mother, and he replied: "My mum was better looking."
She added: "I said 'Can I give you a kiss?' and he said 'You can give me a peck on the cheek', and when Kate came over he said about me 'Watch that woman!'"
When she asked if she could have a hug too, William replied: "Oh, go on then," and posed for a picture with her.
Kate, who wore a baby pink outfit by Lela Rose with trademark wedges, beamed at her fans. William was casually smart in a light-blue checked jacket, shirt, worn without a tie, and blue trousers.
Mrs Moore also told William she had met his late mother, Diana, Princess of Wales, about 25 years ago in nearby Redruth.
She said: "He's lovely. I've just got to meet Harry now, then I've met all of them."
Elsewhere, Kate smiled as she poured a pint of cider during her visit to Healey's Cornish Cyder Farm in Penhallow as part of her day-long tour.
The Duchess laughed as she handed the pint over to her husband.
William and Kate ended their day in Cornwall on Towan Beach in Newquay, where they were greeted by thousands of fans.
The couple were there to see the work of the Wave Project, which uses surfing to reduce anxiety and improve wellbeing in children.
They met children and their mentors from the charity and watched them take part in surfing and lifesaving activities.
Jane Leadbetter, Mayoress of Newquay, spoke to Kate about bringing Prince George and Princess Charlotte to the area.
"She said they would love it here, they do bring them down to Cornwall.
"They surf themselves. I can't remember where she said they surfed but it was two places here," she said.
Her husband, Councillor Carl Leadbetter, the Mayor of Newquay, who welcomed them to the beach, said: "It was absolutely thrilling. It was a delight.
"I welcomed them both to the town and said we are absolutely delighted they are visiting us.
"We talked about surfing. The Prince said he loves to surf and is hoping to do some."
William told children and volunteers on the beach: "We should have brought our wetsuits, I'm very jealous.
"Living by the beach is just perfect."
He later added: "I am feeling really annoyed that I am not in the proper gear."
Victoria Lord, 28, and her daughter Millie, 10, spoke to William and Kate in their swimwear after taking a dip at the beach.
"They were all dressed up and I was in my bikini but it didn't bother me, it was just amazing to see them," said Miss Lord, from Preston.
"I said 'hiya' and William said it was nice meeting all the children."
Millie added: "It was an experience I will never forget."
As they posed for a group photo with children - known as nippers - from three local life-saving clubs, William and Kate giggled as they did the Shake or Gnarly hand gesture, which is associated with surfing.
Bea Hodge, 15, a young farmer from Wadebridge, said: "It was weird because you don't normally see them do things like that.
"I have only ever seen them in a magazine."
Bea spoke to Kate about farming and how important it was that George and Charlotte learned about it.
"She said she was teaching George and Charlotte all about the farm at Sandringham," Bea said.
"She's been teaching George the difference between barley and wheat and everything they grow on the farm there.
"She wants the children to learn all about farming and the apples in their orchard.
"She said she'd secretly like to be a young farmer."
William shared his love for Star Wars with Jaydon Mitchell-Tomlinson, five, who was wearing a T-shirt featuring the films.
Jaydon, who has cerebral palsy and uses a wheelchair, had waited for three hours to see William and Kate with his mother Emma Mitchell.
"He had been really frustrated because he couldn't see them, but then William came over and talked to him about Star Wars," she said.
"Jaydon said his favourite character is Darth Vader, because he's a baddie, and William said he liked him as well."
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