ACR MAKES ILLEGAL INTXN TKOF AFTER TURN ONTO WRONG TAXIWAY.

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TAXIING FOR TKOF; SO SAID WE NEEDED RWY 4R FOR THE WT; (ABOUT 174000 POUNDS). XING 4L; I HEARD TWR SAY; 'CLRED FOR TKOF ON 4R; NEXT (APCHING) ACFT IS LNDG 4L.' CAPT THOUGHT HE HEARD 'TURN L.' INSTEAD OF TAXIING ON AA TO END; HE TAXIED ON A TO WHAT WAS EFFECTIVELY AN INTXN TKOF. HAD THIS BEEN CLR AT THE TIME I WOULD HAVE SPOKEN UP THEN. WE DID THE TKOF; NO PROBLEM. OUT OF 18000 FT I SAID THAT I THOUGHT WE HAD MADE AN ILLEGAL TKOF. HE LOOKED AT CHART AND SAID THAT THE 9300 FT DID NOT INCLUDE THE DISPLACED THRESHOLD AREA ON EACH END. AFTER MUCH DISCUSSION I POINTED OUT BY USING THE SCALE THAT INDEED THAT WAS INCLUDED. WE GAVE AWAY NEARLY 1200 FT OF RWY. CLB WAS NORMAL WITH LOTS OF ROOM; MAY NOT HAVE SEEMED SO WITH ENG FAILURE. ON REFIGURING; SO SAID WE WERE OK FOR 4L; WHICH IS 8200 FT. EVEN SO; WE WERE ILLEGAL WITH NO DATA FOR INTXN TKOF ON 4R. CAPT SAID HE'D NOT USED FULL LENGTH AT SOME OTHER PLACES BASED ON THIS INFO; NAMELY MEXICO CITY. PROBLEM WAS CAUSED BY HIS MISINTERP OF THEIR COMMAND ABOUT 'L'; LACK OF UNDERSTANDING ABOUT RWY LENGTH; MY OWN FAILURE TO IMMEDIATELY ADVISE AND RECOGNIZE. MUCH LEARNED; FORTUNATELY A CHEAP LESSON. A DEADHEADING CAPT ASKED AFTER THE FLT IF WE KNEW WE HAD MADE A MISTAKE.