I have a Macbook pro which is running Mac OS X 10.8.5 (64 bit), and I use the Safari browser. I've downloaded Flash Player 188.8.131.52, and the helper tells me that it has installed, although I can't find an icon or anything else to open it in my 'finder'.
The only thing on my system that differs from the installation help guide, is that in my Safari-preferences option, it just has 'allow plug-ins' (selected) at the bottom of this box, and there is no option for 'allow java' as per your example. I even updated my Java version, and it tells me that this in installed too (version 7, update 67) , although I can't see that in finder either. Any ideas how to fix this?
I've tried uninstalling and re-installing three times now with no success.
Flash Player is not a program that you open by itself, so there is no icon to click to open. It is a plugin used by the browser to view Flash content. To determine that Flash Player is correctly installed, you can navigate to http://helpx.adobe.com/flash-player.html and click the 'check now' widget on the page. This will tell you what version you have (184.108.40.206 is the most current version). There is also an animation towards the bottom of the page that will play if Flash Player is correctly installed on your system.