Explanation:

Alright, let's break it down.

First, let's figure out the pattern for 'COUNTRY' -> 'BOWKXLF':

- C?B: -1

- O?O: same letter

- U?W: +2

- N?K: -3

- T?X: +4

- R?L: -5

- Y?F: +6

So, the pattern is: alternate subtraction and addition, increasing in absolute value. The sequence is: -1, 0, +2, -3, +4, -5, +6.

Let’s apply this to 'DESPAIR':

1. D: 4 -1 = 3 ? C

2. E: 5 +0 = 5 ? E

3. S: 19 +2 = 21 ? U

4. P: 16 -3 = 13 ? M

5. A: 1 +4 = 5 ? E

6. I: 9 -5 = 4 ? D

7. R: 18 +6 = 24 ? X

So, 'DESPAIR' becomes: CEUMEDX.

Check the options:

1. GBPSXIO

2. ULDSVHG

3. GBVMDFU

4. UFDMVBG

Nowhere among the options do we see 'CEUMEDX'. None of the given options match. But, let's check if maybe the coding pattern was different or if there's a calculation twist. Maybe the sequence is: -1, 0, +2, -3, +4, -5, +6 (as found), or maybe alternating -1, +2, -3, +4, etc.

Let’s check if Option 1 matches this pattern with 'DESPAIR':

D?G, E?B, S?P, P?S, A?X, I?I, R?O

No logical pattern.

Let’s try Option 3:

D?G, E?B, S?V, P?M, A?D, I?F, R?U

Again, no obvious pattern fits.

Now Option 4 ('UFDMVBG'):

D?U, E?F, S?D, P?M, A?V, I?B, R?G

Still not matching.

Here's the thing: none of these options fit the observed rule for 'COUNTRY' to 'BOWKXLF'. Maybe the rule's more complicated or involves a different shift per letter.

So, to answer your question directly:

- None of the options match the way the word 'COUNTRY' was coded to become 'BOWKXLF'.

- Option 4, 'UFDMVBG,' doesn't correspond to the deciphered pattern.

- But, going by your answer: