Select the alphanumeric cluster that does NOT share the same pattern as the rest:

The correct option is H6 : K10 : N14.

To find the alphanumeric cluster that does NOT share the same pattern, let us analyze the pattern governing the letter positions in the alphabet along with their corresponding numbers for each given option.

First, consider the alphabetical positions of the letters:
E = 5, F = 6, G = 7, H = 8, I = 9, J = 10, K = 11, L = 12, M = 13, N = 14.

Let us check the pattern in each option step-by-step:

1. G5 : J8 : M11
Letter positions: G (7), J (10), M (13). The letter positions increase by +3 each time (7 + 3 = 10, 10 + 3 = 13).
Numbers: 5, 8, 11. The numbers also increase by +3 each time (5 + 3 = 8, 8 + 3 = 11).

2. E3 : H6 : K9
Letter positions: E (5), H (8), K (11). The letter positions increase by +3 each time (5 + 3 = 8, 8 + 3 = 11).
Numbers: 3, 6, 9. The numbers increase by +3 each time (3 + 3 = 6, 6 + 3 = 9).

3. F4 : I7 : L10
Letter positions: F (6), I (9), L (12). The letter positions increase by +3 each time (6 + 3 = 9, 9 + 3 = 12).
Numbers: 4, 7, 10. The numbers increase by +3 each time (4 + 3 = 7, 7 + 3 = 10).

4. H6 : K10 : N14
Letter positions: H (8), K (11), N (14). The letter positions increase by +3 each time (8 + 3 = 11, 11 + 3 = 14).
Numbers: 6, 10, 14. Here, the numbers increase by +4 each time (6 + 4 = 10, 10 + 4 = 14) instead of +3.

Since the numbers in H6 : K10 : N14 do not follow the +3 pattern shared by all other clusters, it does not belong with the rest.