  Solved is a new puzzle raised by the observation of an enhancement structure
Z(3930) in $\gamma\gamma\to D\bar{D}$. If categorizing Z(3930) as
$\chi_{c2}(2P)$ suggested by Belle and BaBar, we must explain why
$\chi_{c0}(2P)$ dominantly decaying into $D\bar{D}$ is missing in the
$D\bar{D}$ invariant mass spectrum. In this work, we propose that the Z(3930)
enhancement structure may contain two $P$-wave higher charmonia
{$\chi_{c0}(2P)$} and $\chi_{c2}(2P)$. We show that this assumption is
supported by our analysis of the $D\bar{D}$ invariant mass spectrum and
$\cos\theta^\ast$ distribution of $\gamma\gamma\to D\bar{D}$. This observation
would not only provide valuable information of two P-wave higher charmonia
$\chi_{c0}(2P)$ and $\chi_{c2}(2P)$, but also serve as the crucial test of our
novel proposal to the observed enhancement structure Z(3930), especially at the
forthcoming BelleII and the approved SuperB.
