What should a solutions architect do to mitigate any single point of failure in this architecture?

Explanations:

Adding a set of VPNs between the Management and Production VPCs would not mitigate the single point of failure in the current architecture. The single point of failure arises from the existing VPC peering connection, and simply adding VPNs does not address the reliance on this single connection for communication between the two VPCs.

Adding a second virtual private gateway to the Management VPC does not resolve the single point of failure. The Management VPC still relies on a single device in the data center for connectivity through the customer gateway. Moreover, a virtual private gateway can only be attached to one VPC at a time, so this would not create redundancy.

Adding a second set of VPNs to the Management VPC from a second customer gateway device provides redundancy for the Management VPC’s connectivity. This means if one VPN connection fails, the other can still maintain communication with the data center, thus mitigating the single point of failure associated with the current setup.

Adding a second VPC peering connection between the Management VPC and the Production VPC would not mitigate the single point of failure, as both VPCs would still rely on the original peering connection for communication. If the first peering connection goes down, the second would not provide any redundancy for the overall architecture.