The question is asking for decomposition into BCNF. It isn't asking if the decomposition is dependency preserving or not.
$R(ABCD) $
$A \rightarrow C$
$C \rightarrow A$
$AB \rightarrow D$
Here the candidate keys are $AB$ and $BC$.
For decomposing a relation into BCNF, we first find a functional dependency which is not trivial and violates the BCNF property.
We get $A \rightarrow C$, here $A$ is not a superkey, and hence causes a violation of BCNF.
So, decomposing it into $(A, C)$ and $(A, B, D)$. This is now in BCNF. Option (A).
Now if in the first step of "finding a functional dependency which is not trivial and violates the BCNF property", we chose $C \rightarrow A$, we get the following decomposition:
$(C, A)$ and $(C, B, D)$. This is also in BCNF(but does not preserve dependencies). Option (B).
So, both (A) and (B) are correct.