Given the PDA $P = (Q_P,\Sigma,\Gamma_P,\delta_P,F_P)$ and the DFA $D = (Q_D, \Sigma, \delta_D,q_D,F_D)$
What is the 6-tuple definition of the PDA such that: $L(P') = L(P) \cap L(D)$
I don't understand what the intersection of these two FAs represent, and my only guess at what the 6-tuple is would be something along the lines of: $P'=(Q,\Sigma,\Gamma,\delta,q_0,F)$ such that:
$P=Q_P$ x $Q_D$
$\Sigma = \Sigma$
The only other resource on this site I found that is remotely similar to this question is:
Cartesian construction of PDA and DFA
However, I didn't find the answer to be sufficient.