The Flash Player installer will detect a 64-bit system, and automatically install both 32-bit and 64-bit players on it.
What are the symptoms that make you think you have only the 32-bit version?
[topic moved to Flash Player forum]
From what I can find in my control panel (which is the way I check to see what version I have) It continuously shows only the 32 bit version being installed. I'm hunting around and can or could not find anything system wise letting me know I have the 64 bit. The installation file also saying 32 in its name unlike an older version which had 64 bit.