What happens to the L2 portion of a packet when it gets to the first router?

I am reading through this page about networking and had a question about the ARP table portion.

This is the network in question. This is the packet being sent.

I understand that L2 has the host as source and to leave the first network, it has an L2 Destination of the first router. However, once it gets to the Router, the L2 is "complete" right? It reached its destination. However, the packet still needs to make its way over to the Red Network. Does that mean the L2 destination gets written over with the next destinations MAC Address? Thus, does L2 change multiple times through a packet transmission?

Thanks for any insight!