Flight Engineer reported during the procedure to shut down the number 4 engine due to a malfunction they inadvertently shut down the number 3 engine.

Narrative

#3 engine shut down for generator bearing failure light and #4 Engine inadvertently shut down while performing #3 engine shut down checklist.[We noticed] #3 generator out light illuminated along with the #3 generator bearing fail light illuminating.[The cause was] #4 Engine T-handle inadvertently pulled.Generator bearing fail light is cause for engine shutdown. The engine shutdown checklist was implemented with pilot flying calling for '#3 engine condition lever to feather'. The pilot monitoring pointed to the #3 condition lever and I (Flight Engineer) confirmed the proper lever was identified. The pilot monitoring completed the action and #3 engine shutdown normally. The pilot flying then called for the '#3 t-handle; pull'. The pilot monitoring pointed to the #3 t-handle; confirmed by the flight engineer and pilot monitoring completed the action. Right before the t-handle was pulled; the pilot's MFD and co-pilots PFD flashed distracting my eyes (flight engineer) downward. At this point the #4 engine shutdown. A quick scan confirmed the #4 engine t-handle had been pulled. [Priority assistance was requested] and a turn back to ZZZZ was initiated. The #3 engine shutdown checklist was completed. The crew discussed an air start for the #4 engine and decided to attempt. The air start checklist was implemented and a successful air start was accomplished. No further incidents on return to ZZZZ.