The reaction of a tertiary alkyl halide with alcoholic KOH leads to elimination (E2 mechanism), forming an alkene (Y). The addition of HBr in the presence of peroxides follows the anti-Markovnikov rule, leading to (Z). For C\(_4\)H\(_9\)Br, the correct intermediate (Y) is 2-methyl-1-propene, which reacts with HBr (in peroxides) to form 1-bromo-2-methylpropane (Z).