private Game game

"private Game game" means you're declaring a private object of the class Game that is called game.

...Then you'll need to instantiate it in order to make it exist as a real object.

It's just breaking the declaration and instantiation in two different statements. Sometimes it's better to declare an object at the top of your code and then instantiate it when you need it. You can also do both at once.

i think youre missing a little vocab, and i just got it myself. pros out there reading this please correct me if im wrong:

Class Instance = new Constructor("input") Class is the file that you are in with methods to call upon anywhere within the folder, instance is the title of the one specific object you are making right now, theres always a blueprint to construct, but your making the "game" game this time. theres a materials (the Class) but game is the name of what you are building (constructing). the method Game(), or the constructor, is simply a method in the Game class being called on to attatch the input to the object "game".

private Game game; in Class Prompter is to tell people non verbally that Class Game Instance Game is ready, like we had to make: public String answer; for => Game(String answer) to connect "treehouse" to the game. We have to connect the game to the prompter in the same fashion.

i also wonder How is it different from Game game = new Game()??

I think that:

private Game game;

is a declaration of already existing instance of Game class in Hangman.java:

Game game = new Game("treehouse");

but correct me if I'm wrong

It's a constructor. It creates an instance of the game class.