Which of the following letter-clusters will replace the question mark (?) in the given series?
ZG, BD, CX, EO, FC, ?

Let us break the series into two parts: the first letter and the second letter of each cluster.
First letters: Z, B, C, E, F, ?
Let's look at the positional values:

Z = 26

B = 2

C = 3

E = 5

F = 6

Let's check the differences between successive terms:

Z(26) to B(2): +2

B(2) to C(3): +1

C(3) to E(5): +2

E(5) to F(6): +1
The pattern of differences is alternating: +2,+1,+2,+1,…
Therefore, the next difference must be +2.
F(6) + 2 = 8, which corresponds to H.

Second letters: G, D, X, O, C, ?
Let's look at the positional values:

G = 7

D = 4

X = 24

O = 15

C = 3

Let's check the differences:

G(7) to D(4): −3

D(4) to X(24): 4−6=−2≡24 (so −6)

X(24) to O(15): −9

O(15) to C(3): −12
The differences are consecutive multiples of −3: −3,−6,−9,−12,…
Therefore, the next difference must be −15.
C(3) - 15 = -12.
To find the positive equivalent: 26−12=14, which corresponds to N.

Combining both letters, we get HN.