There is a known issue with games like Farmville 2in Firefox 40

https://developer.mozilla.org/en-US/Firefox/Releases/40/Site_Compatibility#Plug-ins

You can turn off the new feature that seems to be causing this issue and see whether that resolves it:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste ipc and pause while the list is filtered

(3) Double-click the dom.ipc.plugins.asyncInit preference to switch its value from true to false

I don't know whether that starts taking effect immediately, or whether you need to exit Firefox and start it up again.

Then return to the page with the game and reload the page (you can click the circular arrow in the address bar) to see whether it will work now.

Any luck?

They made changes to the way Flash loads in FF40, to help speed up pages with videos and flash objects loading, but unfortunately this has messed up some Flash games including Farmville (both 1 & 2).

If you follow the instructions given by jscher2000 above it should fix the problem.

Here are some screen prints to show the actions required - it is really simple

Thank you.