Adobe found a pretty bad bug in the linux 64 bit version of their flash, crafted flash may help a hacker to take over your computer and execute code. Install this only if you know what you are doing.
Finally adobe realised that there are 64 bit machines. not bad it took them only few years.
So the offer a flash plugin for 64 bit.
Now to install it is quite simple for firefox 3
get the file
tar -xvf flashplayer10_2_p3_64bit_linux_111710.tar.gz
sudo cp libflashplayer.so /usr/lib64/
sudo ln -s /usr/lib64/libflashplayer.so /usr/lib64/browser-plugins/libflashplayer.so