I download Hay Hay in 2014 my farm name. is Carolyn farm I have played it now it won't come up on this tablet

If you can install the app you need on that tablet to play it, then I would contact the games creators to find out why you can't access the farm.

Now if you have been playing it through an app on another device that whole time, it is possible the data for your farm is saved on that other device. Rather than the games servers. Again, I would contact them.