Moving this discussion to the Installing Flash Player forum.
This file: Flash Player for ActiveX (Internet Explorer) will install BOTH the 64 bit and 32 bit plugins.
To be sure, run it and afterward, go to: C/Windows/System32/Macromed. You'll see a Flash folder with the associated files.
Go to: C/Windows/SysWOW64/Macromed. You'll see a Flash folder there too, with the associated files.
In the control panel, the Flash Player icon you see says (32bit) because the Global Settings Manager is a 32 bit app. It still manages settings for the 64 bit plugins, though.
If you're using Internet Exploder 11, there's another whole can of worms to deal with.
This is a known problem (Facebook, Yahoo, BBC, CBC, ESPN, Pogo, etc. etc. saying you need Flash Player) with Internet Explorer 11, which Microsoft has been aware of since October 18 when they released their latest "untested" browser. The pages can't recognize the browser, so they don't recognize any of the plugins, like Flash Player. So far, Microsoft has made NO indication that they have any plan to fix it soon.
Microsoft's recommendation is to use Compatibility View for affected pages, and "pretend" you're using an different browser. Trouble with that is it has seen limited success at best, and you have to individually enable it for EVERY page that has problems.
I'm not big on "pretending" so I recommend actually using another browser.
ANY of those will work where IE11 won't, with the Flash Player Plug-in (For all other browsers), and Chrome doesn't even need that because it has its own Flash Player plugin built in.