AN A320 CREW; TAXIING FOR TKOF AT STL; MADE A WRONG TURN ONTO AN ACTIVE RWY WITHOUT A CLRNC.

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TAXI INSTRUCTIONS WERE ISSUED BY STL GND TO TAXI TO RWY 12L; HOLD SHORT RWY 12R AT TXWY C. SUBSEQUENTLY ISSUED INSTRUCTION TO TAXI ACROSS RWY 12R; HOLD SHORT OF RWY 12L. WE PROCEEDED ACROSS RWY 12R AND MISIDENTED TXWY P FOR THE HOLD PAD OF RWY 12L. I (CAPT) MADE THE TURN ON TO TXWY P AND HELD JUST SHORT OF RWY 6/24 WHEN I SAW ANOTHER ACFT ON RWY 6. I IMMEDIATELY STOPPED UNTIL INSTRUCTED BY GND TO CONTINUE ON TXWY C AND HOLD SHORT OF RWY 12L. TKOF AND REMAINDER OF FLT TO ORD UNEVENTFUL. FO DID HIS BRIEFING WHICH I DON'T THINK I LISTENED TO VERY WELL DUE TO OTHER TASKS INTERRUPTING ME. HE WAS TRYING HARD TO KEEP UP AND IN FACT WAS FOLLOWING MY TAXI RTE AND MADE A COMMENT ABOUT WHERE WE WERE GOING. I SHOULD HAVE RECOGNIZED THE TASK SATURATED STATE IN THE COCKPIT AND RESULTANT DECREASE IN THE LEVEL OF SAFETY; BUT WAS 'TUNNEL-VISION' ABOUT GETTING THE ACFT OUT AND FAILED TO STOP THE CHAIN OF ERRORS. HAD I TAKEN A MIN AND RECOGNIZED OUR STATE OF MIND AT THAT TIME AND STOPPED THE ACFT TO GIVE THE FO MORE TIME I FEEL HE WOULD HAVE SEEN MY ERROR AND PREVENTED THE EVENT. SUPPLEMENTAL INFO FROM ACN 557423: AFTER XING RWY 12R AT TXWY C FOR HOLD SHORT OF RWY 12L; CAPT TURNED L ONTO RWY 6/24. I ASKED IF WE WERE CLRED ONTO RWY AND HE SAID NO. WE DETERMINED THAT WE WERE ON AN ACTIVE RWY BY MISTAKE.