DISTRACTED WITH PAX AND INTERPHONE USE AN ACR CAPTAIN INTERPRETS A HOLD SHORT CLRNC TO BE 'POS AND HOLD' RESULTING IN ENTRY ONTO THE RWY WITH AN ARRIVING ACFT ON SHORT FINAL. ANOTHER CREW MEMBER NOTED THE ERROR AND A HASTY CROSSING OF THE RWY IS COMPLETED BEFORE THE ARRIV ACFT'S LNDG.

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TAXI FOR TAKEOFF AT KSLC. DOING BEFORE TKOF CHKLIST; FLT ATTENDANT ADVISED THEY HAD A PAX ON OXYGEN PROB AND NEEDED AN EXTRA MIN. WE PULLED OFF TO SIDE OF TXWY ON FREIGHT RAMP. ALMOST IMMEDIATELY FLT ATTENDANTS ADVISED THEY WERE READY. SO WE PULLED BACK ONTO TXWY AFTER ADVISING TWR WE WERE READY. TWR SAID; (I THOUGHT I HEARD) 'TAXI INTO POS AND HOLD.' ALWAYS; ALWAYS; I LOOK TO MY R AND L TO CLR BEFORE CROSSING RWYS; TXWYS; ETC. THIS TIME I DIDN'T. FO WAS INTO FINISHING UP HIS DUTIES SO HE DIDN'T SEE ME TAXI ONTO RWY 34R. BECAUSE WE WERE HEAVY; I WANTED TO USE ALL THE RWY: THEREFORE; IN LINING UP I SAW TO MY R AN ACFT ON SHORT FINAL. I GAVE THE THROTTLES A SHOVE AND WE CLRED ACROSS THE RWY ONTO TXWY M. LNDG ACFT CONTINUED TO LNDG. IT'S PROBABLE THE TWR SAID 'HOLD SHORT;' BUT I SWEAR I HEAR 'POS AND HOLD;' HEARING WHAT I WANTED TO HEAR MAYBE EVENTS CONSPIRED AGAINST US. THE PAX PROB; ASSOCIATED WITH APCHING TAKEOFF RWY; CHKLIST; AND TWR KEEPING US IN SEQUENCE (WE WERE NUMBER 1 FOR RWY) SO THAT EVERYBODY WAS BUSY; CAUSED ME TO OBVIOUSLY MISS WHAT WAS ACTUALLY SAID. I USUALLY STATE ALOUD WHAT I HEAR ON RWY CLRNC; FROM CTLR TO VERIFY TO MYSELF AND MY FO. THAT WAY IT PROVIDES A BACKUP FOR CORRECTION. I DIDN'T DO THAT THIS TIME TO MY REGRET. ADDITIONALLY; TWR; IN THEIR REPLY; STATED WE WERE STILL NUMBER 1 WHICH MAY HAVE PLANTED THE SEED IN EXPECTATION OF TAKEOFF CLRNC. SUPPLEMENTAL INFO FROM ACN 509908: TWR DIRECTED US TO 'TAXI UP TO AND HOLD SORT OF RWY 34R.' I ROGERED THIS INSTRUCTION AND AS WE MADE A 90 DEG L TURN APCHING THE HOLD SHORT LINE I BEGAN READING THE BEFORE TAKEOFF CHKLIST. WE CROSSED THE RWY 34R HOLD LINE; AND ABOUT RWY CTRLINE A COMPANY B737 ON APPROX A ONE MILE FINAL ASKED TWR IF THE B757 WAS CROSSING. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CALLBACK REVEALED THAT THE RPTR DID NOT USE HIS USUAL CRUTCHES AND REMINDERS FOR TAKEOFF AND CLRED INTO POS VERIFICATION. HE ATTRIBUTES THAT TO THE DISTRACTION OF THE FINISHING UP OF THE PAX PROB AND THE BREAKDOWN IN COORDINATION OF THE COCKPIT CREW BECAUSE OF THE RUSH TO GET UNDER WAY.