Is it possible to create a CFG with succesive palindromes?
A reference to $j$ is missing. My guess is that it should read $x_i=x_j^{\mathcal R}$. This means that some pair $x_i$, $x_j$ should be each others reverse, or one string should be a palindrome. This can be done with a CFG.

(after correction)
It does not say that for each $i$ there should be a $j$, it just states that some $i,j$ exist. One pair will do.  If the word "any" would have been used then this would probably change the meaning, although "any" sometimes is ambiguous.