Step 1: Understanding Jahn–Teller distortion.
Jahn–Teller distortion occurs when degenerate orbitals are unevenly occupied, which causes distortion to remove degeneracy. In octahedral complexes, distortion is strongest for d$^4$ (low spin) and d$^7$ (high spin).
Step 2: Evaluating the options.
(A) d$^5$ high spin → t$_{2g}^3$ e$_g^2$ (symmetrically filled) → no distortion.
(B) d$^5$ low spin → t$_{2g}^5$ (symmetrically filled) → no distortion.
(C) d$^6$ high spin → t$_{2g}^4$ e$_g^2$ → nearly symmetric → weak or no distortion.
(D) d$^4$ low spin → t$_{2g}^4$ (uneven) → strong Jahn–Teller distortion → correct.
Step 3: Conclusion.
Hence, Jahn–Teller distortion is most prominently seen in d$^4$ low spin octahedral complexes.