How long does it take a broken hand bone to heal? Do you think 6 weeks is a good estimate?

4-6 weeks. Most fractures heal within 4-6 weeks. Some are healed enough to start gentle motion exercises within 3 weeks or so. Ask your orthopedic surgeon who can guide you through the healing process and make recommendations regarding safe level of activity.
Yes, 6 weeks. Most fractures are healed by 6 weeks and you should be able to resume normal activities soon thereafter. Most fractures need to be stabilized with a cast or splint. Post immobilization stiffness may require occupational therapy.