I have a little doubt about understanding the basic definiton. Adjacency in strong product of n graphs $G_1, G_2,.....,G_n$ for two distinct vertices $x = (x_1,x_2,...,x_n)$ and $y = (y_1,y_2,...,y_n)$ is defined as .... x and y are adjacent provided that $x_iy_i$ $\in$$E(G_i)$ or $x_i=y_i$ for each 1$\leq$i$\leq$n.
I took the product of $P_4,P_3$ and $P_2$. I labeled the vertices of $P_4$ as 1,2,3,4, the vertices of $P_3$ as a,b,c and the vertices of $P_2$ as x,y. I made vertices (1,a,x),(1,b,y) adjacent as 1=1, a~b in $P_3$ and x~y in $P_2$. Likewise i made adjacent (1,a,x),(1,b,x). But vertices (2,b,x),(4,b,x) cant be adjacent although b=b and x=x but 2 is not adjacent to 4 in $P_4$.