A carbon bearing a methyl and a methoxyl appears in both reactant and product, making a good choice of anchor. We also see in both compounds a carbon bearing an OH sandwiched between a CH₂ and a CCH₃. This gives us the indicated mapping. Thus, we need to break off the Br, make a new bond between C-1 and C-5, and attach a hydrogen to C-6.

AIBN, azo-bis(isobutyronitrile), is a well-known free radical initiator; similarly, tin hydrides are well-known hydrogen atom donors. Again, we have a good start on a mechanism.