Why would your car make a clicking sound when you turn right?

Answer 1

CV joints! If it is a front wheel drive car that is most likely what it is. The boots generally have a tear or are even sometimes missing. (due to rusting) this causes dirt to get up between the joints or even loss of grease with create metal on metal clicking. The noise greatly depends on the speed on which you're turning.

You can generally tell by going underneath your car, and checking the boots. If these are torn and you can see or feel grease, then you need to get it repaired.

A more rare problem could be the spring for the starter. What happens here is that the spring looses its tension, causing it to move back and forth inside the outer casing (it should not move when inspecting). It then hits the flywheel which creates the clicking noise. The only way to fix this is by replacing the whole starter.

(how much that starter wiggles depends on how you're turning)

references: was the problem with my car.