Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster.
IDEOLOGY: YGILIYDC :: HARDWARE : YRUWDRUH :: ISOLATED: ?

Step-1 (find the rule)
Write the first pair one below the other and read the letters of the first word from right to left:

IDEOLOGY → Y G O L O E D I (reversed)
Output in the question: Y G I L I Y D C

The consonants (Y, G, L, D) have remained exactly the same, while every vowel of the reversed form has changed as follows:

O → I, O → I, E → Y, I → C

Each of these changes is obtained by moving 20 places forward (equivalently 6 places backward) in the alphabetical order:
$$O(15)+20=35\equiv9=I,\;E(5)+20=25=Y,\;I(9)+20=29\equiv3=C$$

Apply the same check to the second pair:

HARDWARE → E R A D W R A H (reversed)
After replacing every vowel (E, A, A) by the letter 20 places ahead we get:

E → Y, A → U, A → U → Y R U W D R U H

This is exactly the coded form given in the question, so the rule is confirmed:

Rule:
1. Reverse the letter-cluster.
2. In the reversed string replace every vowel (A, E, I, O, U) by the letter that lies 20 places ahead in the alphabet (equivalently 6 places behind).
3. Keep every consonant unchanged.

Step-2 (apply the rule to ISOLATED)

ISOLATED → D E T A L O S I (reversed)

Now replace every vowel by the 20-ahead letter:

E → Y (5+20=25)
A → U (1+20=21)
O → I (15+20=35≡9)
I → C (9+20=29≡3)

Consonants D, T, L, S stay as they are.

Combining the results: D Y T U L I S C

Hence, ISOLATED is coded as DYTULISC.

Option D which is: DYTULISC