  The goal of this paper is to accurately describe the metastable dynamics of
the solutions to the hyperbolic relaxation of the Cahn-Hilliard equation in a
bounded interval of the real line, subject to homogeneous Neumann boundary
conditions. We prove the existence of an "approximately invariant manifold"
$\mathcal{M}_0$ for such boundary value problem, that is we construct a narrow
channel containing $\mathcal{M}_0$ and satisfying the following property: a
solution starting from the channel evolves very slowly and leaves the channel
only after an exponentially long time. Moreover, in the channel the solution
has a "transition layer structure" and we derive a system of ODEs, which
accurately describes the slow dynamics of the layers. A comparison with the
layer dynamics of the classic Cahn-Hilliard equation is also performed.
