Step 1: Identify the starting compound.
The given structure is phenol \((C_6H_5OH)\).
Phenol is highly activated towards electrophilic substitution and is ortho-para directing.
Step 2: First reaction with \(Zn\) dust.
Phenol on heating with zinc dust undergoes reduction and forms benzene.
\[
C_6H_5OH \xrightarrow{Zn} C_6H_6
\]
So, intermediate \([X]\) is benzene.
Step 3: Reaction with conc. \(HNO_3\).
Benzene reacts with concentrated nitric acid in presence of acid catalyst to form nitrobenzene.
\[
C_6H_6 \xrightarrow{Conc. \, HNO_3} C_6H_5NO_2
\]
So, \([Y]\) is nitrobenzene.
Step 4: Nature of nitro group.
The nitro group \((-NO_2)\) is strongly deactivating and meta-directing.
It directs incoming electrophiles to the meta position.
Step 5: Bromination in dark.
Nitrobenzene reacts with \(Br_2\) in dark (electrophilic substitution).
Due to meta-directing nature of \(-NO_2\), bromine enters at meta position.
\[
C_6H_5NO_2 \xrightarrow{Br_2/dark} m\text{-bromonitrobenzene}
\]
Step 6: Final product identification.
Thus, the final product \([Z]\) is \(3\)-bromonitrobenzene.
Final Answer:
The final product is:
\[
\boxed{3\text{-Bromonitrobenzene}}
\]