Step 1: Understanding the Concept:
A redox reaction involves a change in oxidation number of at least one element, which means electron transfer. If no element changes its oxidation number, it is not redox.
Step 2: Check option (A).
Zn goes from 0 to +2 and H goes from +1 to 0. Oxidation numbers change, so it is redox.
Step 3: Check option (B).
\(\text{Al(OH)}_3 + 3\text{HCl} \to \text{AlCl}_3 + 3\text{H}_2\text{O}\). Al stays +3, Cl stays -1, H stays +1 and O stays -2. Nothing changes. This is an acid-base neutralisation, so it is NOT redox.
Step 4: Check option (C).
Mg goes from 0 to +2 and O goes from 0 to -2. This is redox.
Step 5: Check option (D).
Fe goes from 0 to +2 and \(\text{Cu}^{2+}\) goes to Cu(0). This is redox, a displacement reaction.
Final Answer:
Only reaction (B) has no change in oxidation numbers.
\[ \boxed{\text{(B)}} \]