Examination of each compound:
Phenol:
Phenol, with its electron-donating hydroxyl (OH) group on a benzene ring, is activated towards electrophilic substitution. It reacts readily with bromine, causing decolourisation.
Styrene:
Styrene features a vinyl group (CH=CH2) attached to a benzene ring. The alkene component of styrene undergoes rapid addition reactions with bromine water.
Aniline:
Aniline possesses an activating amine (NH2) group on a benzene ring. Similar to phenol, it undergoes electrophilic substitution reactions with bromine, resulting in decolourisation.
Cyclohexane:
Cyclohexane is a saturated cyclic alkane. Its lack of double or triple bonds makes it resistant to electrophilic attack under normal conditions (reaction typically requires elevated temperatures or UV light). Consequently, cyclohexane does not decolourise bromine water.
Therefore, cyclohexane does not decolourise bromine water.
The compound that does not decolourise bromine water is (4) Cyclohexane.

