$P_2$ and $P_3$ are parallel; $P_1$ and $P_4$ are identical .
Work Step by Step
Two planes are parallel when their normal vectors are parallel. From the give problem,, we see that $P_1$ has a normal vector $\lt 3,6,-3\gt$ or $3\lt 1,2,-1\gt $and $P_4$ has normal vectors $\lt 1,2,-1\gt $are identical because they are multiples of each other. $P_2$ has normal vectors $\lt 4,-12,8\gt $ and $P_4$ has normal vectors $\lt 3,-9,6\gt $ Thus, $P_2$ and $P_3$ are parallel because their normal vectors are in same ratio.