unable to understand the source of error and how to fix it.
Just take your query and look at the first two goals alone:
?- member(b, X), member(d, X).
X = [b,d|_A]
; X = [b,_A,d|_B]
; X = [b,_A,_B,d|_C]
; X = [b,_A,_B,_C,d|_D]
; X = [b,_A,_B,_C,_D,d|_E]
; ... .
Just these two goals produce already infinitely many answers. So no matter what follows, your query will never terminate. By chance, you may happen to get a solution, but more often than not you will end in some loop.
So first of all you need to fix this somehow.
Then consider the meaning of subtract/3 in SWI:
?- subtract([b,d,r], [b,d], [r]).
true.
?- subtract([b,d,X], [b,d], [r]).
false. % ?? why not X = r?
From this alone you can see that subtract/3 is not a relation. So you cannot use it as a relation like, say, append/3.
To fix this and keep as close to your original query, use library(reif) and library(lambda):
?- S1=[b,d,X], S2 = [b,d], tpartition(S2+\E^memberd_t(E,S2),S1,_,[r]).
S1 = [b,d,r], X = r, S2 = [b,d].