By default, a router will not forward any directed-broadcast packets out of any of its interfaces, but only if it recognizes the destination IP as a directed broadcast. Take a look at this diagram once again:
Imagine there is another router, R4, connected to R3, with a subnet of 192.168.34.0/24. If R1 sends a ping to 192.168.34.255, R2 will not recognize the destination as a directed broadcast and will forward it normally. This behavior is described in detail in this post here:
