I had surgery for a broken wrist and torn ligaments or tendons about 6 wks ago. i can't turn a door knob. how long will it take to get better?

It takes time: People who've sustained wrist (distal radius) fractures associated with ligament or cartilage (TFCC) tears can expect it to take several months to heal. At 6 weeks you will have some pain and or discomfort with certain activities. You should start range of motion exercises and incremental grip strengthening. Avoid activities such as push-ups and repetitive forearm motion for 6 more weeks.

Varies: It varies quite a bit. Typically would at best be in the 8-12 week range. Make sure you follow up and follow the instructions of your surgeon, it would seem a little early to be doing things like turning a door knob at this point. Make sure you are being compliant. Your surgeon will be able to tell you more about your specific case.