CARJ FLT CREW WAS ISSUED A CLB CLRNC BY A ZOB CTLR RESULTING IN OPERROR DUE TO CTLR FAILURE TO CLARIFY READBACK.

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I WAS THE PNF AND I RECEIVED A CLRNC TO CLB TO FL220; WHICH I READ BACK. WE WERE HANDED OFF TO ANOTHER CTLR WHOM I CHKED IN WITH AS CLBING TO FL220. AS WE PASSED THROUGH FL210; WE RECEIVED A TA INDICATING TFC WAS 500 FT ABOVE US. THE CTLR SAID; 'ACR X; MAINTAIN FL200; IF YOU ARE THROUGH IT; GO BACK DOWN.' WE WERE ABOUT 1200 FT THROUGH THE ALT WHEN WE WERE ABLE TO REVERSE DIRECTION. WE NEVER RECEIVED AN RA. THE CTLR REDIRECTED THE CONFLICTING TFC AND THE CAPT INQUIRED IF WE HAD BEEN CLRED TO FL220. THE CTLR SAID HE BELIEVED WE HAD BEEN CLRED TO FL200; BUT THAT THE PREVIOUS CTLR ASSIGNED IT. THE CAPT POINTED OUT THAT FL220 WAS OUR FINAL FILED ALT AND THAT WE BELIEVED WE HAD BEEN CLRED TO FL220. THE CTLR WAS NICE ABOUT IT AND EVEN SAID THAT IT MAY HAVE BEEN CTLR ERROR. I WILL ADMIT THAT I WAS TIRED BY THAT POINT; AS IT WAS MY 6TH LEG OF THE DAY THAT STARTED AT XA00 READY RESERVE. TO FOLLOW UP; WE CONTACTED ZOB WATCH DESK AND ZID WATCH DESK AND BOTH CONFIRMED THAT UPON REVIEWING THE TAPES WE HAD IN FACT BEEN CLRED TO FL220 AND I DID READ BACK FL220. SUPPLEMENTAL INFO FROM ACN 653679: I BELIEVED THAT I HAD ASSIGNED FL200 TO THE ACFT I WAS WORKING AND COORD THAT ALT BEFORE XFERRING COM. I HAD ACTUALLY CLBED THE ACFT TO FL220.