At the time, Kate had been speaking with Josh Macpalce, a 25-year-old who is autistic and has DiGeorge syndrome, who was telling her about how he sent her a card for the births of each of her children. He then held out his arms to the duchess and she bent down and said, "Thank you for the hug."
Kate, 38, and William, 37, are parents to 6-year-old Prince George, 4-year-old Princess Charlotte, and 1-year-old Prince Louis.
Hello! Magazine also spoke with Jo Broadbent, who said she spoke to the duchess at the event about her children.
"Kate said Louis had started to tell her, 'mummy, I'm balancing,' and she said it was really nice to see him turning into a little boy from being a baby," Jo said. "She's obviously very proud of her children."
Wednesday marked Kate and Prince William's first joint public outing since last week's drama between her brother-in-law, Prince Harry, and the rest of the royal family. Harry and his wife, Meghan Markle, announced they're stepping back as senior members of the royal family last week.
For more on Kate's life as a mom of three, watch the clip below: