Explanation:

Let’s crack this by figuring out the logic in PATELS : BQFUTM.

Here’s what happens letter by letter:

- P (16th) ? B (2nd): Forward by 1, then modulo 26 isn't fitting. But wait—it’s moving letters to the right by a certain pattern.

- A (1st) ? Q (17th): +16.

- T (20th) ? F (6th): +12 (26+6-20).

- E (5th) ? U (21st): +16.

- L (12th) ? T (20th): +8.

- S (19th) ? M (13th): -6.

But checking every letter, there’s a clear alternating +16, +14, +16, +14, etc. pattern. But the logic is each letter is replaced by the next consonant (PATELS to BQFUTM makes no simple substitution). Let's instead see:

- P ? B (skip to next consonant in the alphabet after "P" is Q, so maybe offset? But B is a vowel.)

Here's the point: The relationship doesn’t follow traditional logic.

So, check if a pattern matches if you try it out with NECTAR:

Let’s compare N-E-C-T-A-R with the provided options:

Look at position-by-position matching:

N ? F (in Option 1 and 2), +8 letters.

E ? O (in Options 1, 2, 3, 4), +10 letters.

C ? U (in Options 1 and 2), +18 letters.

T ? D (in Options 1, 2, 3), -16 letters.

A ? S (in Options 1, 2, 3), +18 letters.

R ? B (in Options 2, 3, 4), +10 letters.

Comparing PATELS : BQFUTM to NECTAR and the transformation in the options, only Option 2, FOUDSB, follows a similar odd shifting pattern to the one seen in the first pair.

- Option 2: FOUDSB

- N?F, E?O, C?U, T?D, A?S, R?B

- This matches the shift style from the first question.

Here’s the thing:

- Option 2 is the only one that follows the same weird jumpy pattern as the original example.

Option 2: FOUDSB is the answer.