Biggest Pallindrome

A pair of strings $(α, β)$ is called a subpair of a string $x$ if $x$ = $x_1+$**$α+$**$x_2+$**$β+$**$x_3$ (where a+b means concatenation of strings a and b) for some (possibly empty) strings $x1, x2$ and $x3$. We are given two strings and we need to find one subpair from each string such that : Let $(a,b) , (c,d) $be subpair of $string1$ and $string2$ respectively and $X$ $=$ $a$ + $b$ + $c$