Explanation:

Let's break it down step by step:

- First Pair (DEMOGRAPHY : EDOMHSPAYH):

- If you look closely, DEMOGRAPHY is not just scrambled; it’s an arrangement:

- The sequence in EDOMHSPAYH selects letters in this order: 1st, 5th, 4th, 7th, 3rd, 8th, 2nd, 9th, 6th, 10th from DEMOGRAPHY.

- D(1), E(5), M(4), O(7), G(3), R(8), A(2), P(9), H(6), Y(10) gives EDOMHSPAYH.

- We need to apply the same pattern to BACKGROUND:

- Assign numbers: B(1), A(2), C(3), K(4), G(5), R(6), O(7), U(8), N(9), D(10)

- Now, using the EDOMHSPAYH pattern:

- 1st: B

- 5th: G

- 4th: K

- 7th: O

- 3rd: C

- 8th: U

- 2nd: A

- 9th: N

- 6th: R

- 10th: D

- Arranged: BGKOCUANRD

- Let's check the options:

- Option 1: DNKCSHUOAB — Doesn't match.

- Option 2: DNKCHSUOAB — Doesn't match.

- Option 3: ABKCHSUODN — Doesn't match given rearrangement.

- Option 4: ABKCSHUODN — Doesn't match.

None of the options match BGKOCUANRD exactly, but let's check if any option listed follows the rearrangement order. On reviewing, none match the rearrangement perfectly.