Step 1: Elimination with Alcoholic KOH \begin{itemize} \item Tert-butyl bromide \((\text{CH}_3)_3\text{CBr}\) undergoes an \(E2\) elimination with alcoholic KOH to form 2-methylpropene \(\big(\text{CH}_2=C(\text{CH}_3)_2\big)\). \end{itemize}
Step 2: Addition of HBr to the Alkene \begin{itemize} \item 2-Methylpropene reacts with HBr via Markovnikov addition, giving back the tertiary bromide, \((\text{CH}_3)_3\text{CBr}\). \item The reaction pathway results in the same tertiary haloalkane as the starting material. \end{itemize} Hence, the major product \((P)\) is \(\text{tert-butyl bromide}\), \((\text{CH}_3)_3\text{CBr}\).