Adobe Flash problem

When I try to play videos I keep getting the message 'You need Adobe Flash to play this video.

The same screen offers a link for downloading Adobe Flash.

I've done this several times. I also note that I do have Adobe XI on my desktop, which I believe is the same thing as Adobe Flash Player.

Accordingly, I should not be getting the message, I believe, and the videos should play.

Does anyone know how to solve this problem?

Merry Christmas to all!

Robert