B747 FLT CREW MISINTERPRETS CLRNC AND TURNS WRONG WAY CAUSING A TCASII RA WHILE ENRTE.

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WE WERE COMPANY FLT XXX. THE CAPT IS FLYING AND I'M ON THE RADIOS; LEVEL FL370; VFR; LNAV; AND VNAV AND AUTOPLT CONNECTED. CAPT GETS UP TO STRETCH HIS LEGS AND TURNS HIS SPEAKER ON; I'M FLYING AND ON THE RADIOS. ZDV ASKS ME TO TURN 40 DEGS TO WHAT I THOUGHT WAS L AND I CONFIRM 40 DEGS TO THE L; OR AT LEAST THAT'S WHAT BOTH THE CAPT AND MYSELF THOUGHT I READ BACK. WE WERE HEADING 057 DEGS AND AS I WAS READING BACK I WAS TURING TO NEW HEADING 017 DEGS. WE WERE ON THIS HEADING FOR AT LEAST 2 MINS WHEN THE CTLR ASKED ME IF I WAS ON A R TURN. I SAID NO. WE TURNED L. HE SAID TURN FURTHER L TO 340 DEGS AND EXPEDITE. I WAS DOING THAT WHEN WE GOT A TCASII RA 'DSND;' I IMMEDIATELY DISCONNECTED THE AUTOPLT AND FOLLOWED THE RA PRECISELY WHILE TURNING; THEN WE RECEIVED A CLR OF CONFLICT. THE CAPT BY THIS TIME IN HIS SEAT HAD ADVISED ATC THAT WE WERE FOLLOWING AN RA. WE THEN CLBED BACK TO FL370 WERE GIVEN HEADING AND CHANGED CTLR; THEN WERE GIVEN PHONE NUMBER FOR ZDV TO CALL. THEY SAID WE WERE ON TAPE AS SAYING R AND TURNING L AND WERE 500 FT AND 2 MI SEPARATION FROM ZZZ.