A KING AIR FLC TAXIES THE WRONG WAY AND CREATES A RWY INCURSION AT PHL; PA.

Narrative

ON A PART 135 FLT AT A MAJOR ARPT; THE COPLT RECEIVED TAXI INSTRUCTIONS. THE GND CTLR WAS VERY BUSY AND ISSUED INSTRUCTIONS VERY FAST. I (CAPT) ASSUMED HE (COPLT) UNDERSTOOD THE CLRNC. AT THE FIRST INTXN; WE TURNED L. I ASKED THE COPLT IF WE WERE CLRED ACROSS A RWY (AT THE TIME ACTIVE; BUT NOT IN USE). HE SAID 'YES' SO WE PROCEEDED ACROSS THE END OF THE RWY. AT THIS POINT THE GND CTLR STOPPED US AND STATED THAT WE HAD 'BLOWN' OUR TAXI CLRNC. WE WERE REISSUED TAXI INSTRUCTIONS AND TOLD TO CALL ATC UPON ARR AT OUR DEST SINCE WE CROSSED A RWY. I KNEW FROM THE ORIGINAL INSTRUCTIONS THAT WE WERE TO HOLD SHORT OF A DIFFERENT RWY; WHICH WE DID. HOWEVER; THE RTE WHICH WE THOUGHT WE WERE SUPPOSED TO TAKE ACROSS A DIFFERENT RWY; WHICH WE WERE NOT TOLD TO HOLD SHORT OF. DUE TO THE HVY TFC; THE CTLR ISSUED INSTRUCTIONS QUICKLY. WE AS A CREW SHOULD HAVE QUERIED AND MADE SURE WE UNDERSTOOD CLRLY THE TAXI INSTRUCTIONS; WHICH WE DID NOT. THE CTLR COULD HAVE BEEN CLRER AND BE A LITTLE SLOWER IN DELIVERING HIS INSTRUCTIONS. I; AS CAPT; SHOULD HAVE NOT CROSSED A RWY UNLESS I WAS ABSOLUTELY SURE THAT I WAS CLRED TO DO SO. AFTER CALLING ATC AND DISCUSSING THE MATTER; NO FURTHER ACTION WAS TAKEN.