Hercules C-130 Flight Engineer reported they had #3 engine generator failure which required a shut down of the #3 engine. They inadvertently shut down the #4 engine.

Narrative

The number 3 engine generator bearing fail light illuminated with loss of the #3 generator. This is an engine shut down condition. Engine shut down checklist bold face procedures commenced. First step is pilot flying calls for the #3 condition lever to be moved to the feather position. The proper lever is confirmed by the flight engineer with the pilot monitoring completing the action. The #3 shut down normally. Next step is the pilot flying calls for the #3 T-handle to be pulled. The proper handle is confirmed by the flight engineer with the pilot monitoring completing the action. The #4 engine shut down unexpectedly at this point. [Advised ATC] and we started our turn back to ZZZ. Troubleshooting for the #4 engine shutting down started and it was discovered that the #4 T-handle had been pulled inadvertently. The crew discussed and determined that there were no prior indications of malfunctions with the #4 engine and it was decided to air start the #4 engine. The air start checklist was run and a successful air start on the #4 engine took place with no further incidents back to ZZZ.