What is proxy ARP?
If an ARP Request packet is sent to a host on a different network, the device connecting the two networks can reply to this packet.
What is routed proxy ARP?
It assures communication between devices on the same network segment but on different physical networks. In practice, it is used if a gateway of a host is not specified.
Taking into consideration the below topology, we can see that both host are on the same network segment.The IP addresses of VLAN 100 and VLAN 200 are on different network segments. It means that each host is in different broadcast domains. That's why the host cannot receive an ARP request packet and cannot reply with an ARP reply packet as well. The router proxy ARP is a solution for this issue.
Add ethernet interfaces to proper VLANs and configure IP addresses of the VLANs. Set IP addresses of the hosts as well. Don't specify a gateway of the hosts: