Problem:
 
I can not install the Adobe flash plug-in for Firefox on x86_64.

 
 
Reason:
 
Adobe has not provided the flash plug-in for x86_64 yet (2008/12/18).
However, there is a workaround: install the i386 flash plug-in by using i386 browser on x86_64.

Flash Player support on 64-bit operating systems: http://www.adobe.com/go/6b3af6c9

 
 
Solution:
 
Install Firefox for i386 on x86_64:

1: Remove the installed  Firefox and some libraries for x86_64.

 
# rpm -e firefox nss nspr evolution28-atk evolution28-cairo evolution28-gtk2 evolution28-glib2 evolution28-pango

2: Once removed, install the same packages and flash-plug-in for i386.

 
# rpm -ivh
firefox-xxx.i386.rpm nss-xxx.i386.rpm nspr-xxx.i386.rpm
evolution28-atk-xxx.i386.rpm evolution28-cairo-xxx.i386.rpm
evolution28-gtk2-xxx.i386.rpm evolution28-glib2-xxx.i386.rpm
evolution28-pango-xxx.i386.rpm flash-plugin-xxx.i386.rpm

Additionally, Adobe has provided the alpha version of their flash plug-in for x86_64 on 2008/12/16. It should be officially provided in the near future.
http://labs.adobe.com/downloads/flashplayer10.html