Mother [topic-は] my room [subject-が] messy [nominalizer-の] [object-を] does-not-like
私の部屋が乱雑なのを好まない — the entire clause 'my room being messy' is nominalized with の and made the object of 好む (to like). 乱雑 (らんざつ) = messy/cluttered. 好まない is the literary negative of 好む.