How broadcast packets get forwarded if router drops it?

first things first
what broadcast packets are you talkin about?
generic broadcast packets are local to a network and are by default dropped by the router. remember - routers are boundary devices.

if a router starts to broadcast l2 and l3 packets beyond a network we will soon be flooded with random arp packets. so by default routers dont forward braodcast packets.

now as always there are expections. you can read about directed broadcasts where router sometimes broadcasts packets beyond a local network