GA SMA UNAUTHORIZED TAXI RWY XING AT PDK.

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ARPT WAS EXTREMELY BUSY; WIND FROM NW; SO PARALLEL RWY 2L WAS NOT IN USE; PARALLEL RWY 2R RESERVED FOR JETS (LONG RWY); RWY 34 USED FOR ALL OTHER ACFT. WE WERE TOLD TO 'CROSS 2L HOLD SHORT OF 2R' (WE DID THAT). AFTER ABOUT 1 MIN; WE WERE TOLD TO 'CROSS 2R; HOLD SHORT OF 34'. IN ORDER TO COMPLY; WE HAD 2 CHOICES: 1) GO STRAIGHT; OR 2) TURN R. EITHER DIRECTION WOULD HAVE ALLOWED US TO CROSS 2R. WE WENT STRAIGHT. AS SHOWN BY DIAGRAM BELOW; ATC (GND) WANTED US TO TURN R; CROSS 2R; AND HOLD AT DEP END OF 34. GND ACTUALLY SAID; 'CROSS 2R' WHICH WE DID AND PLANNED TO HOLD SHORT OF 34 ON E SIDE OF 34 (THERE WAS AN ACFT HOLDING OVER THERE ALREADY). OBVIOUSLY; UNDER THE BUSY CONDITIONS; WE MISUNDERSTOOD; AND CROSSED ACTIVE RWY 34 WITHOUT A CLRNC. I BELIEVE A BETTER INSTRUCTION WOULD HAVE BEEN 'TURN R ON TAXIWAY BRAVO; CROSS 2R; HOLD SHORT OF 34'. IT WAS ANOTHER BREAKDOWN IN COMS; MADE WORSE BY THE EXTREMELY BUSY TFC CONDITIONS. (I HAD A DISCUSSION WITH THE TWR SUPVR UPON RETURNING FROM MY 1.5 HR INSTRUCTION FLT.)