Can I draw 240v out of this configuration?
The feeder wire has a black, a red, a white, and a green so this suggests there are both legs present, i.e., 240 V is present.

There appears to be a double space on the right open for a 2-pole breaker. A 60 A feeder breaker should support the addition of a 2-pole 20 A load depending on the actual loads on the other circuits in this sub-panel.