impulse response cascaded with time reversed of itself
HINT: See what happens in the frequency domain. Convolution corresponds to multiplication. You just have to figure out the Fourier transform of $h[-n]$, expressed in terms of the Fourier transform of $h[n]$. Multiplying the two functions results in the Fourier transform of the convolution of $h[n]$ with $h[-n]$. The result has a special property which makes it very easy to determine its phase.