While visiting Towers Residential Outdoor Education Centre in Betws-y-Coed, Conwy, the royal couple ascended a climbing wall.
Earlier, they visited a photography project run by charity Mind in Caernarfon, Gwynedd.
They also saw the work of GISDA which provides training for young people.
Twm Griffiths, who works at the charity's training centre in Caernarfon, said the couple were rushed off their feet.
He said: "They didn't have time for a coffee. They have a very busy day."
Afterwards, the couple visited the Men's Shed in Denbigh, Denbighshire - a social group involved in community projects.
The pair chatted with a small crowd outside, including four-year-old Esme who presented Prince William with flowers and asked about Prince George.
William said his son was "loud" and thanked her for the flowers, which he said he would give to Catherine.
Men's Shed director Phil Williams said the couple were given a tour of facilities, including an allotment and a woodwork workshop, and were very interested in the project.
Member Alan Maddocks presented them with a gavel and bowl which he carved on a lathe, a skill he has learned since joining the group.
"They were very friendly. On the way out they both shook my hand," he said.

Pleidleisiodd yr Arglwyddi 222 i 222 ar welliant gan y blaid Lafur i Fesur Cymru fyddai'n trosglwyddo cyfrifoldeb dros y berthynas ddiwydiannol mewn gwasanaethau cyhoeddus Cymreig o Lundain i Gaerdydd.
Yn unol â'r drefn pan mae pleidlais yn gyfartal, nid yw'r gwelliant yn cael ei basio.
Byddai colli'r bleidlais wedi golygu y byddai oedi cyn i'r Mesur ddod yn gyfraith am y byddai aelodau seneddol wedi derbyn cais i'w wyrdroi.
Dywedodd llefarydd y blaid Lafur, y Farwnes Morgan o Drelai ei bod wedi ei siomi'n fawr gyda'r canlyniad.
Byddai'r gwelliant wedi galluogi Llywodraeth Cymru i gael gwared ar rannau o'r Deddf Undeb Masnach sydd wedi bod yn ddadleuol.
Mae disgwyl i aelodau'r Cynulliad ym Mae Caerdydd roi eu sêl bendith i Fesur Cymru ddydd Mawrth nesaf.
The Duke and Duchess of Cambridge have been in north Wales to meet organisations which support young people and tackle mental health issues.
[NEXT_CONCEPT]
Fe wnaeth llywodraeth y DU osgoi colli pleidlais o drwch blewyn yn Nhŷ'r Arglwyddi nos Fawrth dros welliant i Fesur Cymru.