AN A300 CARGO FLT PIC TURNS THE WRONG WAY ON TXWY M WHEN DIRECTED TO RWY 21C AT DTW; MI.

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TAXIING ACFT FROM CARGO TO RWY 21C; I MISTAKENLY TURNED R ON TXWY M; INSTEAD OF L TO GET TO RWY. (WENT TOWARDS RWY 3C INSTEAD OF RWY 21C.) CIRCUMSTANCES: RWY 21R WAS CLOSED; HAD TO CROSS THEN CONTACT CLRNC DELIVERY FOR A REROUTE. AS CAPT; I WAS TRYING TO LISTEN TO 2 DIFFERENT FREQS AND WAS DISTRACTED. COPLT WAS RECEIVING CLRNC AND NOT BACKING UP TAXI RTE. CONFUSION DEVELOPED INCLUDING COPLT TURNING MY GND FREQ TO SOMETHING ELSE. ALSO THERE WAS A HOT MIKE ON GND TO ADD TO IT. CORRECTIVE ACTION WAS TO TAKE ONE TXWY UP AND BACK TAXI. JUDGEMENT SHOULD HAVE BEEN TO WAIT TILL THE END OF RWY AFTER TAXI AND GET CLRNC. RECOMMENDATION: WE RECEIVE INITIAL CLRNCS ON ACARS. WHY CAN WE NOT RECEIVE AMENDED CLRNCS THE SAME WAY. COULD SAVE ACFT FROM A POSSIBLE CONFLICT. BOTH PLTS COULD DIRECT ATTN TO THE IMMEDIATE AND NOT BE SEPARATE. COULD USE A CERTAIN PASSWORD OR CODE THAT AMENDED CLRNC RECEIVED BY ACARS. SUPPLEMENTAL INFO FROM ACN 484122: TAXIED OUT OF BLOCKS THE FIRST TIME AFTER ALMOST BEING DELAYED DUE TO A MAINT PROB THAT HAD TO BE DEFERRED. A FLT WARNING COMPUTER HAD FAILED RESULTING IN INCREASED CREW WORKLOAD DUE TO THE NEED TO MONITOR ACFT SYS. THEN WE HAD TO RETURN TO THE BLOCKS BECAUSE OF WX RELATED DEP HOLDS FOR OUR DEST ARPT. WE WERE THEN INSTRUCTED BY GND CTL TO TAXI TO RWY 21C (A RWY DIFFERENT FROM THE ONE WE HAD PLANNED FOR; THUS REQUIRING PERFORMANCE DATA RECOMPUTATION; FLT MGMNT SYS REPROGRAMMING; AND TAXI RTE REEVALUATION.) HE MONITORED BOTH FREQS (CLRNC DELIVERY AND GND CTL). BEFORE GOING OVER TO GND CTL; I CHKED THE ARPT DIAGRAM FOR THE NEW TAXI RTE AND SAID; 'LOOKS LIKE A PRETTY STRAIGHT FORWARD RTE TO RWY 21C;' TO WHICH THE CAPT REPLIED;' YES; IT DOES.' (NOTE: NEITHER CREW MEMBER ACTUALLY DESCRIBED THE SPECIFIC TAXI RTE INTENDED. LATER DISCUSSION REVEALED THAT THE CAPT WAS THINKING OF A R TURN AT TXWY M WHILE I WAS THINKING OF A L TURN.) UPON REACHING THE TURN POINT; THE CAPT BEGAN A R TURN ONTO TXWY M. I LOOKED UP AND SAID; 'WHICH DIRECTION ARE WE GOING? AREN'T WE SUPPOSED TO BE TURNING L?' IMMEDIATELY THEREAFTER; GND CTL CALLED AND SAID; '(CALL SIGN); YOU ARE TURNING THE WRONG WAY.' THE CAPT; RECOGNIZING THE ERROR; ACKNOWLEDGED THE CALL AND THEN REQUESTED AND RECEIVED A NEW TAXI CLRNC TO RWY 21C. LATER; DURING OUR CREW DEBRIEF; THE CAPT AND I AGREED ON THE FOLLOWING LESSONS LEARNED: BE ESPECIALLY CAUTIOUS WHEN BURDENED WITH INCREASED WORKLOADS. WHEN BEHIND SCHEDULE; RESIST THE TENDENCY TO RUSH (SUCH AS; BY TRYING TO MONITOR TWO FREQS SIMULTANEOUSLY. WAIT UNTIL ACFT IS STOPPED; THEN MONITOR). WHEN RECEIVING CHANGES; IE; RWY; DON'T ASSUME; CONFIRM INTENTIONS. DURING TAXI; IF BOTH PLTS ARE UNABLE TO PROPERLY MONITOR THE TAXIING BECAUSE OF OTHER DUTIES; IE; PERFORMANCE COMPUTATIONS; FMS CHANGES; ETC; MONITOR NOW; ACCOMPLISH OTHER DUTIES LATER (WHEN STOPPED).