2006 Prius clicking when turning right or left.

That sounds like the classic drive axle symptoms each drive axle has a boot and a joint at each end of the shaft you can either jerk your originals out of the car and run it to a place in your town that will put new joints on your original shafts and new boots for whatever that rate is or there's probably a place close to you or in your town or you can take your original joints and shafts what you take out of your car take them to this place and for $89 or something like that they'll hand you a shaft with two new joints and two new boots all ready to go they'll put it side by side with the one you brought in and show you it's the same and all that and send you on your way or at least that's the way it is in the automotive area in the southeast that I live in. If not you can buy the joints and boots at your parts store and beat them off your shafts and put the new ones on I generally opt to just buy the rebuilt shafts locally if possible there is a place here that specializes in driveline axles drive shafts and all of it they have equipment to build and balance truck drive shafts aluminum the whole nine The last time I bought rebuilt drive axles from them I think on my dealer account they were $69 a pop. I'm listed as Barnett's engineering out of Durham North Carolina I have accounts with a lot of suppliers and distributors If it gets you a discount have at it

 

Does this clicking require the car to be moving, or were you getting a click just by turning the steering wheel back and forth with the car stopped?

CV joint clicks would be strong suspects if the car was moving. If the car was still, your clicks were probably from something in the steering column itself: possibly the U-joints in the intermediate shaft.

 

You should jack up both A arms and support them with jack stands then put the car in drive to see if you can hear any kind of 'clicking' Sometimes the clicking will not be evident as their is no load on the CV axles but still you should investigate just to see.
Another is the steering shaft which could also give a similar sound but usually more subtle. You should check it with the engine off and try to detect any hints of clicking or play in the steering column while turning right/left.

 

The last Car Care Nut video briefly mentions an emerging electric power steering clunk that is fixed under the dash. But if my next lunch was on the line, I would bet the cv joints.

 

Depending on the lunch, I might pay attention to whether the CV joints are or aren't turning at the time the sound is made.