If you have a 240VAC circuit that has a neutral (typically would have 4 pins on the plug, line1, line2, neutral, and ground), then it's trivial to pull 120VAC from it safely. If you only have line1, line2, and ground (no neutral), it's also easy to do so it "works", but I'd say it's not safe to do and certainly would not meet code working only at the outlet (you would also need to do work inside the service panel).
The pic you included only has 3 pins exposed, so you'd need to pull the outlet out and see if it was fed with a 3-conductor (plus ground) or 2-conductor (plus ground). Mostly likely the latter, so you'd have a small amount of work to do on the service panel side as well. (Generally, switch to a single pole breaker, and put one of the now line conductors to the neutral bus bar, blank off the opening left by the now narrower breaker, and change the outlet in the room.)