DC9 PIC MISUNDERSTOOD TAXI CLRNC AND CROSSED RWY 12R WITHOUT CLRNC. FO HAD READ BACK CORRECT CLRNC.

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WHILE TAXIING FROM OUR GATE TO HOLD SPOT D WE WERE TOLD TO CONTACT GND CTL; WHICH WE DID. THE GND CTLR TOLD US TO FOLLOW AN MD80 FROM R TO L AT TXWY E. WE SAW 2 MD80'S AND ASKED FOR CLARIFICATION. THEY SAID TO US TO TURN R AND PROCEED BEHIND THE MD80 AT TXWY E. THAT ACFT WAS HOLDING SHORT OF RWY 12R AT TXWY E. RWYS 12R&L WERE ACTIVE RWYS. GND CTL TOLD THE MD80 TO CROSS RWY 12R AT TXWY E; AND TOLD US TO TAXI TO TXWY A AND R ON TXWY C; HOLD SHORT OF RWY 12R AT TXWY C. THE FO ACKNOWLEDGED THIS. I DID NOT HEAR; TURN L ON TXWY A; BUT THOUGHT I HEARD TURN L ON TXWY C; WHICH I FOUND ON THE OTHER SIDE OF RWY 12R. I CROSSED RWY 12R BEHIND THE MD80. GND CTL SAID TO US THAT HE WANTED US ON TXWY C WHICH WAS OFF MY L. THEN ANOTHER CTLR TOLD US TO CALL THE TWR WHEN WE GET TO OUR DEST. AS I TAXIED ACROSS RWY 12R; I SAW OUT MY L WINDOW THE LNDG LIGHTS OF AN APCHING ACFT; SO I EXPEDITED ACROSS. AFTER REACHING CRUISE ALT I TALKED THIS OVER WITH THE FO. UPON FURTHER EXAMINATION OF THE TAXI DIAGRAM; I THEN REALIZED WHAT THE CTLR WANTED US TO DO. UPON REACHING THE DEST ARPT I CALLED STL TWR ON THE PHONE AND SPOKE WITH THE SUPVR. I APOLOGIZED AND SAID I REALIZED WHAT MY MISTAKE WAS. HE WAS NICE ABOUT IT AND SAID THERE WAS NO VIOLATION OF SEPARATION; BUT IT WAS CLOSE. HE SUGGESTED THAT THERE MUST HAVE BEEN SOME CONFUSION IN OUR COCKPIT BECAUSE THE FO READ THE CLRNC BACK CORRECTLY. I AGREED AND REMEMBERED THAT WHEN IN DOUBT; DON'T MOVE THE ACFT UNTIL BOTH PLTS AGREE ON THE INSTRUCTIONS. THIS WAS A VERY GOOD LESSON FOR ME. THE CTLR AGREED AND SAID THAT THERE WOULD BE NO VIOLATION BECAUSE OF NO VIOLATION OF SEPARATION; MY PROMPT PHONE CALL AND MY ATTITUDE.