A BE-200 PLT INADVERTENTLY DSNDED TOO LOW AND RECEIVES A TCASII TA.

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I WAS ABOUT 10 MI SW OF EMPORIA VOR AT FL240. MY CLRNC WAS TO FLY THE JHAWK 4 ARR TO OLATHE; JOHNSON COUNTY EXECUTIVE ARPT (ATC). AT THIS POINT ZKC ISSUED ME A DSCNT CLRNC THAT I UNDERSTOOD AS' DSND AND MAINTAIN ONE TWO THOUSAND. AFTER LEAVING FL230 YOU ARE CLRED DIRECT TO JOHNSON COUNTY EXECUTIVE ARPT'. UPON HEARING ONE TWO THOUSAND; I IMMEDIATELY ENTERED 12000 INTO THE ALT SELECT. I MISSED THE SECOND PART OF THE CLRNC AND HAD TO ASK FOR CLARIFICATION. I THEN READ BACK THE ENTIRE CLRNC AND REPORTED OUT OF FL240. AS MY DSCNT PROGRESSED THROUGH 15000 FT; ZKC TOLD ME THAT THERE WAS BARON TFC AT 1 O'CLOCK POS AND I MISSED THE MI BUT I NOTED THE TFC ON MY TCASII AT ABOUT 1 O'CLOCK POS AND 4-5 MI. CTR SAID; 'WHEN YOU GET BY HIM I'LL HAVE LOWER.' I ADMIT I MISSED THIS CUE. I ALSO NOTED THAT THE TFC WAS PASSING WELL TO MY R AND I TRIED TO LOCATE THE BARON VISUALLY BUT DID NOT. ZKC REQUESTED ME TO TURN IMMEDIATELY L 40 DEGS AND SAY ALT. I COMPLIED WITH THE TURN AND RPTED 12500 FT. AT THAT POINT I NOTED THE TFC APPEARED ABOUT 7 MI TO MY R AND AT NO TIME DID I GET TFC ALERT WARNING. ZKC THEN ADVISED ME THAT I WAS TO HAVE LEVELED AT 14000 FT.