Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?
FZN 4 XRF 6 PJX 9 HBP 13 ?

The correct option is ZTH 18.

To find the missing letter-number cluster in the series FZN 4, XRF 6, PJX 9, HBP 13, ?, we break down the logic into the number pattern and the letter pattern.

1. Number Pattern:

Let's observe the sequence of numbers:

4, 6, 9, 13, ?

4 + 2 = 6

6 + 3 = 9

9 + 4 = 13

Following this pattern of adding consecutive integers (+2, +3, +4, +5):

13 + 5 = 18

2. Letter Pattern:

By taking positional values of letters in the English alphabet (A = 1, B = 2, ..., Z = 26):

First Letter:

F (6) - 8 = X (24)

X (24) - 8 = P (16)

P (16) - 8 = H (8)

H (8) - 8 = Z (26)

So, the first letter is Z.

Second Letter:

Z (26) - 8 = R (18)

R (18) - 8 = J (10)

J (10) - 8 = B (2)

B (2) - 8 = T (20)

So, the second letter is T.

Third Letter:

N (14) - 8 = F (6)

F (6) - 8 = X (24)

X (24) - 8 = P (16)

P (16) - 8 = H (8)

So, the third letter is H.

Combining all elements, the cluster that replaces the question mark (?) is ZTH 18.