Based on the English alphabetical order, three of the following four letter-cluster pairs are alike in a certain way and thus form a group. Which is the one that does not belong to that group?
(NOTE: The odd man out is not based on the number of consonants/vowels or their
position in the letter cluster.)

The correct answer is LD - XF.

To determine the letter-cluster pair that does not belong to the group, let us analyze the positional values of the English alphabet (where A = 1, B = 2, ..., Z = 26) for each letter in the pairs.

Let us examine each option step-by-step:

1. TM - HP:
First letter-cluster: T (20), M (13)
Second letter-cluster: H (8), P (16)
Look at the pattern between corresponding letters:
First letters: T (20) to H (8) ⇒ $20-12=8$
Second letters: M (13) to P (16) ⇒ $13+3=16$

2. WP - KS:
First letter-cluster: W (23), P (16)
Second letter-cluster: K (11), S (19)
First letters: W (23) to K (11) ⇒ $23-12=11$
Second letters: P (16) to S (19) ⇒ $16+3=19$

3. ZS - NV:
First letter-cluster: Z (26), S (19)
Second letter-cluster: N (14), V (22)
First letters: Z (26) to N (14) ⇒ $26-12=14$
Second letters: S (19) to V (22) ⇒ $19+3=22$

4. LD - XF:
First letter-cluster: L (12), D (4)
Second letter-cluster: X (24), F (6)
First letters: L (12) to X (24) ⇒ $12+12=24$ (or $12-14\equiv 24$ in cyclic alphabet context, which differs from -12)
Second letters: D (4) to F (6) ⇒ $4+2=6$ (instead of +3)

All pairs except LD - XF follow the consistent rule where the first letter decreases by 12 (-12) and the second letter increases by 3 (+3).

Therefore, LD - XF is the odd one out.