C172 LNDG AT BUR DID NOT HEAR INSTRUCTION TO HOLD SHORT OF A RWY IN USE BY A B737.

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ON THIS PARTICULAR FLT; MY STUDENT AND I WERE APCHING BURBANK ARPT FROM THE SW AT APPROX 6 MI OUT. MY STUDENT CONTACTED THE TWR AND THE CTLR ISSUED US A 'CLRNC TO LAND ON RWY 8; HOLD SHORT OF RWY 15.' MY STUDENT REPLIED WITH 'CLRED TO LAND RWY 8 ROGER;' I IMMEDIATELY TOLD MY STUDENT THAT THE CTLR WANTS A READBACK OF THE HOLD SHORT INSTRUCTIONS; AND JUST AS QUICK; THE CTLR ASKED US TO REPEAT THE 'HOLD SHORT INSTRUCTIONS.' WE DID. AS WE CONTINUED TOWARDS THE ARPT; AN ACR Z B737 'CHKED IN' OVER VNY AND WAS INBOUND TO RWY 8. THERE WAS ALSO ANOTHER ACR Y B737 INBOUND FOR RWY 15. THE CTLR NOW HAD A PROB. WE WERE INSTRUCTED TO MAKE R TFC FOR RWY 15 AND WE ACKNOWLEDGED THE INSTRUCTIONS. NOW THE NEXT INSTRUCTION WE RECEIVED WAS TO CHANGE BACK TO RWY 8. WE WERE TO FOLLOW THE ACR Y B737; AND ANOTHER C172. AT THIS POINT WE WERE NOW NW OF THE RWYS AND TURNING L TO ENTER THE L DOWNWIND FOR RWY 8. OUR FINAL CLRNC WE RECEIVED WAS FOLLOW THE 'ACR Y B737; HEAD STRAIGHT FOR NUMBERS; CLRED TO LAND RWY 8.' WE COMPLIED; AND SINCE WE DID NOT RECEIVE ANY HOLD SHORT INSTRUCTIONS; I WAS UNDERSTANDING THAT WE HAD THE FULL LENGTH OF RWY WAS AVAILABLE. AS WE TOUCHED DOWN; WE STILL HAD A LOT OF AIRSPD FROM MAKING A HASTY APCH TO THE NUMBERS; THIS HAD US ROLLING DOWN PAST THE RWY INTXN. I ALWAYS LOOK TO THE L AND R AS WE COME UP ON THE INTXN; AND SURE ENOUGH; I SAW THE VERT STABILIZER; OF AN ACR Y B737; OVER THE TOPS OF THE AIRPLANES PARKED ON THE RAMP; MOVING DOWN RWY 15; HEADING TOWARDS US. I IMMEDIATELY TOOK THE CTLS AND BEGAN BRAKING AS HARD AS I COULD. THE CTLR YELLED THROUGH THE RADIO 'EXPEDITE YOUR ROLL THROUGH THE INTXN!' FORTUNATELY; THE B737 WAS ALSO BRAKING HARD AND WE MISSED EACH OTHER.