Changing a 240v plug with 4 wires to 240v plug 3 wires
It looks like your wires are in conduit.  You need to follow the wires a bit more and figure out what they're being used for.  They should go back to a circuit breaker, and it should be a 2-pole (240V) breaker.  Turning off that breaker should turn off two of the wires.  I have no idea what's going on with the third (black) wire.

Those are the two wires to put on L1 and L2 on your NEMA 6-20 receptacle.  The ground goes to ground obviously.  NEMA 6 does not use neutral.