The question asks which word contains the /o/ sound (the closed o vowel, as in the French word beau).
The correct answer is eau. The French spelling eau is always pronounced /o/. This is one of the standard graphemes for the /o/ sound in French, alongside au, ô, and word-final o.
The other options produce different vowel sounds:
eut (past historic of avoir) is pronounced /y/ - the same vowel as in tu or lune.
eux (them) is pronounced /ø/ - the closed eu sound, a rounded front vowel distinct from /o/.
eu (past participle of avoir) is pronounced /y/, the same vowel as eut.
The key distinction: eau = /o/ (a back rounded vowel), while eu = /y/ (a front rounded vowel). These are entirely different sounds despite their similar spellings.