While reading this question, I found that the answers did not address the point I had come for. On planes with electronic propeller synchronization, how is it actually accomplished? I know why propeller synchronization is useful but I am curious about the mechanisms behind how it works.
I fly a large 4-engine turboprop. It uses constant speed hydraulic props, which automatically change blade angle to maintain 1020 rpm. The sync box (which I was unable to find a picture of) takes inputs from each engine's tachometer generator (where it gets the RPM signal) and a pulse generator, which is a magnetic pickup right behind the prop. There is a magnet on the number 1 blade of each prop. With this information, the solid state logic components inside the sync box can slightly change blade angle by sending power to the speed derivative servomotor. This is different from the answer that @davidinnes provided, but I suspect that he's correct for the type of propellers he's familiar with. The sync system on the P-3 also takes inputs through a potentiometer attached to the power levers, and can start increasing or decreasing blade angles if you change your power setting quickly. It works faster than the hydromechanical system and lessens RPM overshoots and undershoots as the prop works to get back to 100% rpm.
In this picture you can see syncrophasing in action. The props are all slightly out of phase with each other, which reduces noise and vibration. #2 and 4 look pretty close, but it's far from a perfect system. You can definitely tell the difference from the cockpit when it's working well. Again as @davidinnes mentioned, you can adjust the system to the change where the point of minimum (or maximum) noise is in the cabin. We call it "running the buzz" up and down the tube, and it's a great way to annoy a navigator that you don't like
By modulating the fuel flow to the slave engine, ie the one which is to synchronise to the "master" engine, Note. Limited authority of fuel modulation and not permitted in Take off or approach.
One writer alluded to synchrophasing to not only reduce beating bit alos reduce noise, You can as I have done move the point of minimum noise around/along the cabin by small changes in phase angle. Actual angle (relative position of the prop blades) depends on number of blades per engine, Easy with two engines, more than 2 ,,, its more of an art
I've been told that the flight engineer's position in a B-17 was such that he could look out a window and shine a strobe light at the prop blades on one side of the plane. The strobe was slaved to one of the engines and the engineer could use the strobe light to tweak all the other engines into sync manually.