AN ACR BA31 MISINTERPED THE DSCNT CLRNC GIVEN BY THE ARTCC RADAR CTLR AND CAUSED A LTSS INCIDENT. CTLR MISSED THE INCORRECT READBACK DUE TO WORKLOAD; BUT CAUGHT THE ERROR WHEN HE SAW THE BA31 START HIS DSCNT. AN ACR MD88 BELOW THE BA31 RESPONDED TO A TCASII RA TO DSND; BUT THE SEPARATION WAS ALREADY LOST.

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FIRST ACFT WAS GIVEN A CLRNC TO CROSS 10 MI S OF FLAT ROCK AT 15000 FT; WHICH IS SOP FOR THE NEXT SECTOR. SECOND ACFT WAS CLBING OUT OF RICHMOND TO 14000 FT (FILED FOR FL310) FOR THE XING TFC. THE SECOND ACFT WOULD CLB TO FL200 AFTER MISSING TFC AS PER SOP. FIRST ACFT READ BACK XING RESTR CORRECTLY. AFTER APPROX 1 MIN; FIRST ACFT CALLED TO VERIFY TO CROSS 10 MI S OF FLAT ROCK AT 10000 FT. THE CTLR (I WAS ASSISTING) HEARD 15000 FT AND STATED 'AFFIRMATIVE.' WHEN FIRST ACFT LEFT 15000 FT; THE RADAR CTLR VERIFIED HIS ASSIGNED ALT AS 15000 FT. THE ACFT STARTED BACK UP AND STATED HE THOUGHT HE WAS CLRED TO 10000 FT. CAUSE: CTLR WAS VERY BUSY AND HEARD WHAT HE EXPECTED. SUPPLEMENTAL INFO FROM ACN 387731: WHILE CRUISING AT 17000 FT; ZDC ISSUED A CLRNC TO DSND TO 15000 FT 10 MI SW OF FLATROCK VOR. CAPT READ BACK CLRNC. WHEN DISCUSSING THE CLRNC IN COCKPIT; CAPT THOUGHT THE CLRNC WAS DSND TO 10000 FT 10 MI S OF FLATROCK. CREW DECIDES TO CONFIRM CLRNC WITH ZDC. CAPT CALLS CTR TO CONFIRM THE CLRNC WAS TO 10 MI SW OF FLATROCK AT 10000 FT. CTR STATES 'AFFIRMATIVE.' CREW SETS 10000 FT IN ALT ALERTER AND FMS. UPON REACHING 14600 FT; ZDC CALLS TO CONFIRM WE ARE LEVEL AT 15000 FT. ABOUT THE SAME TIME; THE TCASII ALERTED OF TFC. AT 14500 FT FO IMMEDIATELY STARTS CLB BACK TO 15000 FT. CAPT EXPLAINS TO CTR WE THOUGHT THE CLRNC WAS TO 10000 FT. CTLR STATES CLRNC WAS TO 15000 FT. MD88 CALLS SAYING THEY STARTED A DSCNT DUE TO TCASII ADVISORY. FLT CONTINUES AS NORMAL FROM THIS POINT. THERE WAS CONFUSION IN THE COCKPIT AS TO WHAT ALT THE FLT WAS CLRED. CREW MEMBERS DISCUSSED CLRNC AND DECIDED THEY SHOULD CONFIRM THE ALT WITH ZDC. WHEN CAPT ASKED THE CTLR TO CONFIRM; THE CTLR JUST STATED 'AFFIRMATIVE.' THINGS WERE BUSY FOR THE CTLR AND I THINK HE THOUGHT WE WERE TRYING TO CONFIRM THE DISTANCE FROM THE VOR AS OPPOSED TO THE ALT. IF THE CTLR RESTATED THE CLRNC AS ORIGINALLY STATED THIS CONFLICT MAY HAVE BEEN AVOIDED.