AIR TAXI PLT OF C402 HAS NMAC WITH B737 BOTH ON APCH TO XING RWYS. HE MISUNDERSTOOD HIS BASE TURN INSTRUCTIONS.

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MCCARRAN ARPT WAS LNDG AND TAKING OFF USING RWYS 1L AND 7R. APCH CTL WAS USING RWY 1L FOR JET ACFT/ACRS AND RWY 7R FOR SMALLER ACFT. I; IN A C402 FOR ACR X; WAS COMING FROM THE SE. APCH HAD INSTRUCTED ME TO RPT A MID-FIELD R DOWNWIND FOR RWY 7R. ONCE I WAS ON THE R DOWNWIND FOR RWY 7R; APCH INSTRUCTED ME TO TURN MY BASE E OF THE FINAL APCH PATH FOR RWY 1L. I MISUNDERSTOOD MY INSTRUCTIONS AND THOUGHT ATC SAID TO TURN MY BASE W OF THE FINAL FOR RWY 1L. IN ADDITION; MY PAX WERE DISTRACTING ME BY BLOCKING MY VIEW WHILE I'M LOOKING FOR TFC AND CONSTANTLY TAPPING MY SHOULDER TO ASK QUESTIONS. SO I CONTINUED W PAST THE FINAL APCH OF RWY 1L AT ABOUT 4000 FT MSL. BEFORE TURNING BASE; TWR QUERIED ME ON MY ACTIONS; INFORMED ME OF MY ERROR AND TOLD ME TO FLY DIRECT TO RWY 7R. ONCE ON MY MODIFIED FINAL FOR RWY 7R; TWR RPTED TFC AT MY 2-3 O'CLOCK POS; A B737 ON FINAL FOR RWY 1L. I HAD HIM IN SIGHT AND CONTINUED MY APCH. I KEPT MY APCH HIGH TO AVOID A CONFLICT. ONCE ON SHORT FINAL; I DID SEE THE B737 PASS UNDER ME. THE LNDG OCCURRED WITHOUT EVENT. GND CTL TOLD ME TO COPY DOWN A PHONE NUMBER AND CALL THEM ON A LAND LINE. ON THE TELEPHONE; THEY TOLD ME OF MY ERROR AND THAT THE B737 HAD TO DROP 200 FT OF ALT ON FINAL BECAUSE OF A TCASII ALERT. AN INVESTIGATION IS PENDING.