Does the sixth train station stop at 34th street penn station?

What are you talking about? If you mean the 6th Avenue trains, they stop one long block away at 34 St and 6th Avenue. If you mean the #6 train, it stops about 7/8 of a mile away at 33 St. and Park Avenue South. Neither stops right in Penn Station. Only the 7th Avenue and 8th Avenue trains do that.