It would seem you have a very, very old version of Flash Player installed. If you're using multiple browsers you may not have the correct plugin installed, as Internet Explorer uses the ActiveX Control, Firefox uses NPAPI plugin, and Chrome/Opera (and other Chromium-based browsers) use the PPAPI plugin.
Since you're now using IE, launch IE and navigate to https://helpx.adobe.com/flash-player.html. Click the Check Now button and post the resulting System Information in your reply.
Also, what is the website you are going to to download the game and what is the name of the game? What Service Pack if any, do you have installed?
Thank-you for the reply.
I clicked the Check Now button and these were the results:
Your Flash Version 126.96.36.199
Your Browser Name Internet Explorer (Active X)
Your Operating System Windows (Vista)
The game I am trying to download is called Nancy Drew. I do not know what you mean by a service pack. I'm sorry I can't be more specific.