How to make a Post Machine for $a^nb^n$?
This language $a^nb^n$ can be recognized by a one counter automaton,
i.e. a pushdown automaton with only one kind of stack symbol (other than the stack bottom).

That can be easily mimicked by a Post machine (with capital P, like
Turing), according to the Wikipedia definition.

So first try to design the PDA with a single stack symbol (that is
easy), and then translate it to a Post machine.

But I am not sure you are using the same type of Post machine as described in Wikipedia, and you did not describe your model.