Tertiary butyl cyclohexyl ether on treatment with $\mathrm{HI}$ forms tertiary butyl iodide and cyclohexanol.

$S_{N}1$ mechanism is followed as the tertiary carbocation formed is stable.

The iodide nucleophile gets attached to the tertiary carbon atom to form tertiary butyl iodide and the cyclohexyl group that is connected to oxygen forms a bond with hydrogen coming from the dissociation of hydrogen iodide to form cyclohexanol.

The equation of the reaction is:

Hence, the answer is option D.