Algorithmics course, please explain thoroughly, I'm trying to understand.

3. (standard, 20pt) Let be an alphabet. Given two words w1 and w2, a match between w1 and w2 is a word w satisfying w1=w1w and w2=ww2 for some w1 and w2. Given two languages L1 and L2, we use L1L2 to denote the set of matches between w1 and w2 for all w1L1,w2L2. Prove that if L1 and L2 are regular languages, then so is L1L2