facebook fan page

how to make a fanpage on facebook so that there is in the forum?

Add the url of the fanpage in
Display>Generalities
Homepage message
message content:

Or else add it in some widget.

Some a widget a forum

What are you asking?

More about Forum widgets.
https://help.forumotion.com/t22589-forum-widgets

how to make like the following picture?

Maybe you get the code from facebook which when added, you will get something like this.

if I can do? please provide a simple way ... !! Naturally, I am a newbie

I am not sure, make a facebook page & check.

yes that is something that has to be on facebook with facebook developers tools, you will have to create a account with facebook as a developer then find out what it's called.
then it will just be a script/code you add and will have to add your facebook app id they facebook provides.

INFO ADDED
I am not sure if you will need a developers account for that or not,
But you will need an app id, and i think when you go through the steps for that it puts in in for developers account. I cant remember it's been a while, either way you will have to go through the steps for the directions facebook provides

I think what you have in the screen shot may be called facepile?

https://developers.facebook.com/docs/plugins/