Pilot reported during cruise they had a #3 engine generator bearing failure and had to shut down the engine. While accomplishing the engine shut down procedure; they inadvertently shut down the #4 engine.

Narrative

After leveling off at FL240 the MFD and FO's PFD went black. The flight engineer stated 'bearing failure light number three generator'. At that point I disconnected the auto pilot while calling for the number three engine condition lever to Flight Engine rather; this was confirmed by the flight engineer. I called for the number three T-handle pull; this was confirmed by the flight engineer and I heard it pulled. After which; I knew something was not correct. I glanced at the engine RPM indicators for both three and four and both were at zero. I asked why is number four feathered? I heard 'it's not'. I responded by saying 'yes; it is; look at the RPM's'. At this point I hadn't realized why it was feathered. I asked the FO to [advise ATC] due two engines shut down; and request a decent and direct to ZZZ. I then looked at the T-handles and saw that the number four T-handle was pulled. The check lists were completed. I asked for number four to be restarted. Restart was accomplished and we landed in ZZZ safely. I observed that the crew was frazzled by what had occurred; and kept a cool head while getting them back into the flying game. After returning to ZZZ I debriefed the crew. We talked about what had occurred and how to prevent this in the future and lessons learned from this. When I asked if the FO's hand was pointing to the number 3 T-handle the flight engineer said that it was but that the FO's hand was under the number 4 T-handle.An inadvertent shut down of the incorrect engine by the T-handle. While it was confirmed it was not visually verified resulting in the incorrect engine being shut down resulting in two engines being shut down. We need to be training to evaluate and assess situations and respond accurately rather than regurgitating a memorized response to every challenge. It is my belief that the system failed. Our training can improve so these situations will not occur in the future. While it's not possible to cover every situation or how one reacts; we can strive to slow ourselves down. The system failed! The individual failed. The question remains; why?