Let's analyze each compound:
Phenol:
Phenol contains an electron donating group (OH) attached to a benzene ring, activates the ring toward electrophilic substitution. Phenol readily undergoes electrophilic substitution reactions with bromine, leading to decolourisation.
Styrene:
Styrene contains a vinyl group (CH=CH2) attached to a benzene ring. The alkene part of styrene will readily react with bromine water by addition reaction.
Aniline:
Aniline also contains an activating amine group (NH2) attached to a benzene ring. It readily undergoes electrophilic substitution reactions with bromine, leading to decolourisation.
Cyclohexane:
Cyclohexane is a saturated cyclic alkane. It lacks double or triple bonds and isn't readily susceptible to electrophilic attack (it would require much higher temperatures and/or UV light to react). So Cyclohexane does not decolourise bromine water under normal conditions.
Therefore, cyclohexane does not decolourise bromine water.
The compound that does not decolourise bromine water is (4) Cyclohexane.
Total number of possible isomers (both structural as well as stereoisomers) of cyclic ethers of molecular formula $C_{4}H_{8}O$ is: