  The decay widths of four-body double-pion decays $\ds\to pn \pi^0\pi^0$,
$\ds\to pn \pi^+\pi^-$, and iso-scalar parts of $\ds\to pp \pi^0\pi^-$ and
$\ds\to nn \pi^+\pi^0$ are explicitly calculated with the help of the $d^*$
wave function obtained in a chiral SU(3) quark model calculation. The effect of
the dynamical structure on $\ds$'s width is analyzed both in the single
$\Delta\Delta$ channel and coupled $\Delta\Delta$ and $CC$ channel
approximations. It is found that in the coupled-channel approximation, the
obtained partial decay widths of $\ds\to pn \pi^0\pi^0$, $\ds\to pn
\pi^+\pi^-$, and those of $d^*$ to the iso-scalar parts of $pp \pi^0\pi^-$ and
$nn \pi^+\pi^0$ are about $7.4$MeV, $16.4$MeV, $3.5$MeV and $3.5$MeV,
respectively As a consequence, the total width is about $64.5$MeV. These widths
are consistent with those estimated by using the corresponding cross section
data in our previous investigation and also the observed data. But in the
single $\Delta\Delta$ channel approximation, the widths are still almost
2-times larger than the measured values. Apparently, the explicitly calculated
width together with the evaluated mass of $d^*$ in the coupled $\Delta\Delta$
and $CC$ channel approximation can well explain the observed data, which again
supports our assertion that the $\ds$ resonance is a six-quark dominated exotic
state.
