VFR PLT 3 MI OUT FROM FBK AT 4000 FT IS INSTRUCTED TO LAND STRAIGHT-IN RWY 6. PLT RESPONDED UNABLE.

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I WAS APCHING FBK FROM THE W AND APCH AT FAI INSTRUCTED ME TO FLY OVER FAI AT OR ABOVE 2500 FT AGL WHILE TRANSITIONING TO FBK. FBK WAS USING RWY 24 AS ACTIVE. WHEN I WAS ABOUT 4 NM FROM FBK; APCH TOLD ME TO SWITCH FBK TWR. AFTER SWITCHING TO TWR; I WAS INSTRUCTED 'CLR TO LAND.' AT THIS TIME I WAS DSNDING THROUGH 5000 FT MSL. I INFORMED TWR THAT THEY HAD NOT ASSIGNED A RWY TO ME YET. TWR INFORMED ME TO WAIT A MOMENT. AFTER A PAUSE; TWR CAME BACK AND TOLD ME TO LAND STRAIGHT IN RWY 6. THIS PUT ME ON A 3 MI FINAL AT ABOUT 4000 FT MSL. I INFORMED TWR THAT I WAS TOO HIGH TO MAKE A STRAIGHT-IN FOR RWY 6 AND REQUESTED RWY 24. AFTER PAUSING AGAIN; TWR INSTRUCTED ME TO MAKE MODIFIED BASE TO RWY 6. NOW I WAS 2 1/2 MI FINAL RWY 6. I INSTRUCTED TWR THAT THERE WAS NO WAY I COULD MAKE RWY 6 FROM MY ALT. TWR PAUSED AGAIN AND TOLD ME TO ENTER DOWNWIND RWY 24. AS I ENTERED DOWNWIND; I WAS DSNDING THROUGH 2500 FT MSL TO PATTERN ALT AND NOTICED ANOTHER ACFT FLYING IN SAME DIRECTION IN LEVEL FLT COMING OUT OF SUUS GLAVE. WE MAY HAVE COME WITHIN 400-500 FT OF EACH OTHER. TWR THEN ASKED IF I WAS ACFT ON L DOWNWIND FOR RWY 24. I SAID THAT I WAS AND THAT I HAD TFC ABOVE ME. I WAS THEN CLRED TO LAND. THINKING BACK; TWR MAY HAVE INSTRUCTED ME TO ENTER R DOWNWIND FOR RWY 24; NOT L.