Is that Br supposed to be a CH2Br?? Because if not the CH2 seems to come out of mid air. If it is CH2Br, then the Br leaves forming a carbocation on the primary carbon...but thats no so stable so it rearranges (not sure if its a methyl shift or hydride shift or none of the above) so the carbocation is on a secondary carbon forming that larger ring rather than the ring with a methyl off of the bridgehead carbon. Then and E1 reaction proceeds removing an H from the carbon thats not a bridgehead carbon to form the product shown. If it removes an H from the bridghead carbon, the product violates bredts rule which says that a brigded bycyclic compound cannot have a double bond at the bridgehead position unless its over 8 carbons big. Ill draw it up if i can.
This is the best i could come up with...I do remember something special about silver nitrate, but im not sure what it is. Im also not 100% sure how the rearrangement goes about, but I think thats just the only rearrangement that will give you a double bond that doesnt violate bredts rule. You would think the hydride shift would occur at the 3* carbon because that is more stable, but all the E1 products formed from the 3* bridgehead carbon as a carbocation violate bredts rule.
**seems there might be another rearrangement to give the final product instead of what I drew...I dont know why that would happen. It might rearrange again to have the middle carbon in the bridge to have the + charge so that it could form a double bond with either of its adjacent carbons instead of where I have the + charge can only form the double bond with 1 adjacent carbon?? Im not sure, I could be way off.