Last online indicator

If you use a browser, then it's the lower right corner (light gray, the wheel icon) then Turn Off Chat (click and make sure it's not checked).

I'm not talking about that ... i am talking about on mobile devises how it shows that you are online or the last time you where.

What your phone model? Which app/browser you use?

i think it happens on any mobile devise if they have the messenger app installed

So you use Facebook Messenger. Then it's pretty difficult, as Messenger was designed to be on the whole time (with PUSH notifications). You have to do multiple steps in Android (clear data, means you have to type in your login info again), and a full uninstall in Apple. In essence, pretty much not very useful.
So first you have to ask yourself, do you even want to use Messenger?
Yes - do a lot of things everytime you want to go offline, do some more stuff when going back online.
No - use third party apps (like Friendcaster), that do NOT integrate Messenger functionality

No,  I don't even use messenger. but, the people who do can see that i am online. That is the problem

Then you use the official Facebook app ? Uninstall, and use third party (like Friendcaster)
Also, after that, use a computer, start a browser, go to facebook, settings, security, "Where You're Logged In", End all activity.

Jacqueline ,

I think that might be what i need.

ty