Step 1: Identifying zero magnetic moment.
Zero magnetic moment occurs when the metal center in the complex has no unpaired electrons. This can happen when the metal is in a low-spin configuration with all electrons paired.
Step 2: Conclusion.
Thus, the correct answer is option (D).
Final Answer:
\[
\boxed{\text{(D) } [Fe(NH₃)_6]Cl_3}
\]