Step 1: Hybridization of the central atom.
- In \( \text{Ni(CO)}_4 \), the nickel atom undergoes sp\(^3\) hybridization.
- In \( [\text{PtCl}_4]^{2-} \), the platinum atom also undergoes sp\(^3\) hybridization.
- In \( \text{XeO}_2\text{F}_2 \), xenon undergoes sp\(^3\) hybridization.
- In \( \text{XeF}_4 \), xenon undergoes sp\(^3\)d\(^2\) hybridization.
- In \( [\text{SF}_4]^{2-} \), sulfur undergoes sp\(^3\)d hybridization.
- In \( [\text{Co(NH}_3)_6]^{3+} \) and \( [\text{Co(H}_2\text{O})_6]^{3+} \), cobalt undergoes d\(^2\)sp\(^3\) hybridization in both cases.
Step 2: Conclusion.
The pair of compounds with the same hybridization for the central atom is (4) \( [\text{Co(NH}_3)_6]^{3+} \) and \( [\text{Co(H}_2\text{O})_6]^{3+} \) as both involve the central cobalt atom with d\(^2\)sp\(^3\) hybridization.