  A model for the pion photoproduction on nuclei in the $A\left({\gamma ,\, \pi
NN} \right)B$ reaction is presented. This is an extension of our recent model
for the $A\left({\gamma ,\, \pi N} \right)B$ reaction. In this approach we have
moved beyond the standard shell-model considering $\Delta$\textit{N}
correlations in the nuclear wave functions, which are caused by the virtual
transitions $NN \to \Delta N \to NN$ in the ground state of the nucleus. The
main ingredients of the model are the two- and three-particle density matrices
and the transition operators $\gamma \Delta \to N\pi $ and $\gamma N \to N\pi
$. The direct and exchange reaction mechanisms, which follow from the structure
of the density matrices, are examined. The model is used to investigate the
$^{12}$C$\left({\gamma ,\, \pi ^{+} p} \right)$ and $^{12}$C$\left({\gamma ,\,
\pi ^{-} p} \right)$ reactions in the kinematic region of the large momentum
transfers to the residual nuclear system, where the pion production occurs with
the emission of two nucleons.
