Step 1: Work out the coding rule.
This is a letter to number coding question built only on the vowels of each word. A value is fixed for every vowel:
\[
A=1,\ E=2,\ I=3,\ O=4,\ U=5
\]
Consonants get no value at all. To connect a pair of words, pick out only the vowels in each word, in the order they appear, replace each vowel with its number, and add the numbers up. If the two totals match, the words are linked.
Step 2: Check the totals for the given pair COMPATIBLE and CURIE.
The vowels in COMPATIBLE, in order, are O, A, I, E.
\[
4+1+3+2=10
\]
The vowels in CURIE, in order, are U, I, E.
\[
5+3+2=10
\]
Both totals come out to 10, so CURIE is the word whose vowel sum matches COMPATIBLE. This confirms the coding rule: the paired word must carry the same vowel sum as the given word.
Step 3: Find the vowel sum of AUDIENCE.
The vowels in AUDIENCE, in order, are A, U, I, E, E.
\[
1+5+3+2+2=13
\]
So the answer we are hunting for must be a word whose vowels add up to 13.
Step 4: Test every option against the target sum of 13.
FREQUENT has the vowels E, U, E:
\[
2+5+2=9
\]
This does not equal 13, so it is ruled out.
OCEANIC has the vowels O, E, A, I:
\[
4+2+1+3=10
\]
This also falls short of 13, so it is ruled out.
UNDERGONE has the vowels U, E, O, E:
\[
5+2+4+2=13
\]
This matches the target sum exactly.
UNSEEN has the vowels U, E, E:
\[
5+2+2=9
\]
This does not equal 13 either, so it is ruled out.
Step 5: Final Answer.
Only UNDERGONE carries a vowel sum of 13, the same as AUDIENCE, so it is the word that is coded the way CURIE was coded from COMPATIBLE.
\[
\boxed{\text{UNDERGONE}}
\]