AN SMA PLT MISINTERPRETED A TAXI CLRNC AND TAXIED TO THE WRONG RWY AT ZZZ.

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I TAXIED TO RWY 09R AT ZZZ. WHILE TAXING TO RWY 09R I CROSSED RWY 09L/27R. WHEN I CALLED READY TO SOUTH TWR THEY WERE CONFUSED AND TOLD ME I WAS SUPPOSED TO BE AT RWY 27R AND THAT THE TWR OPERATOR HEARD GND CTLR CLR ME TO RWY 27R. AT ZZZ ARPT YOUR CLRNC IS RECEIVED ON FREQ 121.1. WHEN I CALLED IN THEY TOLD ME TO GO TO TWR FOR VFR CLRNC WHEN READY TO TAXI. I CALLED IN ON FREQ 121.75 SOUTH TWR. THEY CLRED ME TO TAXI AND GAVE ME VFR CLRNC EXCEPT FOR THE SQUAWK. I READ BACK CLRNC; THEN; INTERRUPTED FOR SQUAWK CHANGE. I DO NOT REMEMBER READING BACK THE RWY OR HOLD SHORT INSTRUCTIONS. I DO REMEMBER HEARING RWY 9; BUT IT COULD HAVE BEEN RWY 29 AS THERE WAS A CARGO ACR GOING TO RWY 29. THE NORTH TWR WAS ON FREQ 118.3; BUT NOT IN CTL OF TAXI PROC. THE LCL VFR DEP FROM XA00 TO XI00 IS OFF RWY 9R TURN 140 DEGS OR 180 DEGS. AS THIS IS PUBLISHED I DID NOT QUESTION WHAT I THOUGHT WAS CLRNC TO TAXI TO RWY 9R. SEVERAL FACTORS CONTRIBUTED TO THIS INCURSION. FIRST; FAILURE TO READ BACK TAXI INSTRUCTION; AND FAILURE TO CHALLENGE THIS FAILURE. PLT WAS TIRED FROM ALL NIGHT FLT. TWR OPERATOR WAS CTLING ALL POS; AS WELL AS TWO AIRFIELDS; ONE OF WHICH HE COULD NOT SEE GND TAXI OPERATIONS. LASTLY; A MEDICAL CREW MEMBER WAS IN COPLT SEAT AND DID NOT OBSERVE STERILE PROCS.