ZDC CTLR EXPERIENCED OPERROR AT FL270 WHEN DISTRACTED BY OTHER SECTOR DUTIES AND ASSUMING ACFT WAS AT OTHER THAN ACTUAL ALT.

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X AT FL270 LNDG AOO HANDED OFF TO RO3. RO3 CALLED D-SIDE AND SAID 'TAKE DOWN TO 240 AND GIVE TO RO1;' I THOUGHT Y WAS AT FL280; GAVE X FL240. WENT TO TAKE CARE OF A SITUATION IN THE EASTERN HALF OF SECTOR. I GOT BACK TO WESTERN HALF OF SECTOR. NOTICED THE CONFLICT AND TOOK ACTION; TURNED Y TO 360 DEGS AND CLBED TO FL270. TOLD X TO EXPEDITE THE DSCNT. SUPPLEMENTAL INFO FROM ACN 760532: MOR CALLED AT THE D-SIDE POS AND REQUESTED THAT THE AOO ARR BE TAKEN TO FL240 AND HANDED OFF TO EKN. I RELAYED THIS INFO TO THE R-SIDE. AT THIS POINT; MY D-SIDE TRAINER STARTED TO REVIEW THE SOP FOR AOO ARRS AND WHY THEY SHOULD BE AT FL270. AFTER THIS; A FEW THINGS HAPPENED THAT HAD TO DO WITH THE FREQ COVERAGE AND SEVERAL CLRNCS HAD TO BE REPEATED. THE CONFLICT ALERT STARTED GOING OFF WHEN X WAS OUT OF FL267 FOR FL240. THE RADAR CTLR HAD GIVEN THE DSCNT TO FL240 WHILE MY TRAINER AND I WERE REVIEWING THE SOP. THE RADAR CTLR TOOK EVASIVE ACTION; AND THE E145 RESPONDED TO THE TCAS ALERT AFTER THE RADAR CTLR HAD TURNED HIM OUT TO AVOID THE KING AIR.