the 6th gym is saffron city - enter saffron by obtaining tea from the old lady in celadon and offering it to the guard in the house on route 7. open the gym by defeating team rocket/giovanni in silph co.
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In Pokemon FireRed and LeafGreen you can't open a gym.
You will find the key to the Gym of Cinnabar Island, From the Pokemon Mansion that is on the same island.
I think the gym in fuschia city
After defeating Blaine at Cinnibar Gym, you must return to Viridian City. The gym will now be open, and after defeating the leader, you'll get the Earthbadge.
The sixth gym leader,Sabrina, is in Saffron City.