1. Shut down Firefox
2. Run the following commands from a terminal...
sudo apt-get remove flashplugin-*
sudo apt-get remove nspluginwrapper
3. Click the link at the very bottom of this page...
http://labs.adobe.com/downloads/flashplayer10.html
...to download the latest 64-bit Flash plugin. Save it to your Desktop and extract it to your Desktop.
Drag libflashplayer.so from the extracted folder onto your Desktop.
4. Run these commands from the terminal...
mkdir -p .mozilla/plugins
mv ~/Desktop/libflashplayer.so .mozilla/plugins
5. Restart Firefox
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