A B737-700 FLT CREW RPTED THAT THEY MISHEARD BNA GND CAUSING THEM TO CROSS RWY 31 AT THE WRONG TXWY.

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AFTER PUSHBACK; I CALLED FOR TAXI CLRNC AND WAS TOLD TO EXIT T5; T3; TXWY K TO RWY 2L. I ASKED IF RWY 31 WAS AVAILABLE AND WAS TOLD THAT IT WAS NOT. I TOLD THE CAPT WHILE STILL ON THE RAMP THAT I WOULD BE HEADS DOWN WHILE I REVISED THE NUMBERS AND FMC DATA TO REFLECT THE CHANGE IN RWY. I REVISED THE NUMBERS AND WENT HEADS UP JUST AS WE WERE XING RWY 31. THAT APPEARED OK BECAUSE OUR CLRNC INVOLVED XING RWY 31. I REALIZED THAT WE WERE XING RWY 31 AT T5 RATHER THAN AT T3 JUST AS ATC TOLD US THAT WE HAD CROSSED AT THE WRONG INTXN AND TO TURN R AT TXWY K; CROSS THE APCH END OF RWY 20C TO RWY 2L; WHICH WE THEN COMPLIED WITH. THERE WAS NO CONFLICT WITH OTHER TFC. SUPPLEMENTAL INFO FROM ACN 593131: RECEIVED TAXI INSTRUCTIONS THAT I THOUGHT WERE EXIT SPOT T5; TAXI TO RWY 2C. FO READ BACK TAXI INSTRUCTIONS TO GND AND ASKED FOR RWY 31 DEP. GND SAID RWY 31 WAS CLOSED. I BEGAN TO TAXI FROM GATE XX AND FO ASKED IF I WANTED HER TO CHK PERFORMANCE AS WE HAD SET UP FOR RWY 31 DEP. I SAID YES; THINKING THE RAMP AREA WAS A GOOD PLACE TO CHK PERFORMANCE. FO TOLD ME WHEN SHE WAS HEADS DOWN WORKING. I BEGAN TO TAXI TO SPOT T5; CROSSED RWY 31 APCHING TXWY K. GND CALLED AND SAID THOSE WERE NOT THE TAXI INSTRUCTIONS HE THEN GAVE US TAXI K; TAXI B; RWY 2L. I THINK THE PROB WAS I WAS EXPECTING RWY 31 FOR DEP AND DIDN'T LISTEN PROPERLY TO GND INSTRUCTIONS FOR FO READBACK. I DIDN'T HAVE A BACKUP AS THE FO WAS HEADS DOWN WORKING.