Instead of the dummy variable _ just use another variable X1 and ensure it does not unify with X.
count([],X,0).
count([X|T],X,Y):- count(T,X,Z), Y is 1+Z.
count([X1|T],X,Z):- X1=X,count(T,X,Z).
However note that the second argument X is supposed to be instantiated. So e.g. count([2,23,3,45,23,44,-20],23,C) will unify C with 2. If you want the count for every element use
:- use_module(library(lists)).
count([],X,0).
count([X|T],X,Y):- count(T,X,Z), Y is 1+Z.
count([X1|T],X,Z):- X1=X,count(T,X,Z).
countall(List,X,C) :-
sort(List,List1),
member(X,List1),
count(List,X,C).
Then you get
?- countall([2,23,3,45,23,44,-20],X,Y).
X = -20,
Y = 1 ? ;
X = 2,
Y = 1 ? ;
X = 3,
Y = 1 ? ;
X = 23,
Y = 2 ? ;
X = 44,
Y = 1 ? ;
X = 45,
Y = 1 ? ;
no