Changing Dryer outlet to L6-20

Advice greatly appreciated. I have a dryer outlet that i no longer need. It is a 30-R-30A non-grounding receptical. It has 2 hot, 1 common wire connected to it. The breaker is 2 pole 120/240V 30 amp.
Instead of using the dryer outlet, I would like to put in a L6-20-R. We are plugging to a device that requires 240V. But it only has, what appears to be 2 hots, 1 ground.
So I am confused … how can this outlet work w/out a common wire? Can I just hook up the 2 hots, 1 ground, leave out the common and it work or is it more complicated than that?

Contact a local licensed electrician for your work. To post information regarding issues such as these for someone who does not know enough about electricity could lead to an injury.

Ditto

You need to have some knowledge of electrical work if you want to install this receptacle. There is an additional wire that is needed and you cannot use the existing breaker. If you aren’t aware of why these things are needed to be done, hire someone who does. Unfortunately this is not a DIY site.

Jeff