Show that the regular languages are closed against taking "the second half"
Hint: if $L$ is regular, the reversal $L^R$ of the language $L$ is regular; see How to show that a &quot;reversed&quot; regular language is regular.  You should be able to use this fact.

Alternative hint: guess the middle point (non-deterministically), then...

Since this is an exercise problem, I am giving only a hint, not a full solution.  Try solving it yourself.