The reaction involves the formation of a benzyl radical (C$_6$H$_5$CH$_2$) and subsequent halogenation in the presence of Br$_2$. This reaction is typical of a benzyl halide formation, which is carried out under oxidative conditions such as with CrO$_3$ (Chromium trioxide) at high temperatures.
The oxidation of the alkyl side chain (X) to form a benzyl group (C$_6$H$_5$CH$_2$) is facilitated by CrO$_3$, and then the electrophilic bromination leads to the formation of Y (C$_6$H$_5$CH$_2$Br).
Thus, the correct reagent and conditions for this transformation are CrO$_3$ at 773 K and 10-20 atm, making option (4) correct.