AN AIRLINE CREW; DSNDING INTO SEA; OVERSHOT A STAR XING RESTR.

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AS THE PF; CRUISING AT FL310 ZSE ISSUED A DSCNT PER PLT'S DISCRETION TO FL240. DSCNT WAS DELAYED DUE TO HEADWINDS. LATER ZSE ISSUED A DSCNT VIA THE OLYMPIA 3 ARR LNDG S. TO THE BEST OF OUR RECOLLECTION THE FO ACKNOWLEDGED ZSE'S CLRNC TO DSND BY STATING 'LEAVING THREE ONE ZERO FOR ONE TWO THOUSAND.' AT APPROX 13500 FT MSL ATC DIRECTED US TO STOP OUR DSCNT AND INFORMED US WE SHOULD BE AT 16000 FT MSL XING THE OLYMPIA VOR. I IMMEDIATELY INITIATED A LEVELOFF; STOPPING THE DSCNT BTWN 12500 FT AND 13000 FT MSL; WHILE SIMULTANEOUSLY MONITORING TCASII INSTRUMENTATION; NO TFC DISPLAYED; NO EVASIVE ACTION NECESSARY. THE FLT WAS CONTINUED TO A NORMAL LNDG. WE CONDUCTED A DEBRIEFING BTWN THE 2 OF US AND WAS UNABLE TO DETERMINE CONCLUSIVELY HOW THE 12000 FT WAS INADVERTENTLY PLACED INTO FLT GUIDANCE ALT CTL PANEL AND REMAINED SO UNDETECTED. HOWEVER; A POSSIBLE SCENARIO AS TO WHAT MIGHT HAVE TAKEN PLACE. JUST AS I BEGAN MY INITIAL DSCNT TO FL240; WE RECEIVED FURTHER ATC CLRNC TO DSND VIA THE OLYMPIA 3 S ARR; BECAUSE I WAS MANUALLY UTILIZING THE FLT GUIDANCE VERT SPD TO DSND THE ACFT AND ITS CLOSE PROX TO THE FLT GUIDANCE ALT SELECTION KNOB; I MAY HAVE SELECTED 12000 FT; THEN THE FO MAY HAVE BEEN INFLUENCED BY THAT VISIBLE NUMBER WHEN HE STATED 'LEAVING 310 FOR ONE TWO THOUSAND;' DURING THE DSCNT THE 12000 FT WAS NOT QUESTIONED BECAUSE IT WAS 1 OF 2 VALID ALTS (12000 FT AND 16000 FT) THAT SHOULD BE SELECTED DURING THAT PORTION OF THE DSCNT FOR THE XING ALT AT OLYMPIA ON THE OLYMPIA ARR.