How to write a regular expression to match a string that starts with the same pattern that it ends with
Since you asked how to approach it, a good starting point for these sorts of problems is to start by understanding the language.  Try writing down all words in the language of length 1; all words of length 2; all words of length 3; all words of length 4; and see if you can spot any possible patterns (about which words are in the language and which aren't).  Then, see if you can prove your guess.

Finally, use that to help you brainstorm ideas for how to express this as a regular expression.

Make sure to read How to prove a language is regular? carefully.