The key requirements are: limited IP space (192.168.0.0/20), reaching on-premises (172.16.0.0/16) from multiple Google Cloud regions (us-west1, europe-central1, asia-southeast1), and minimizing IP addresses used. The Cloud Interconnect connection to on-premises is in us-east4.

Minimize IP addresses and centralized NAT: Since all traffic to on-premises will traverse the Cloud Interconnect in us-east4, it's most efficient to configure a single Private NAT gateway instance in us-east4. This allows resources from other regions to egress to on-premises through this single NAT gateway, using a minimal NAT subnet (192.168.1.0/24 in this case), thus conserving the limited 192.168.0.0/20 IP space.

Network Connectivity Center Spoke Export Policy: The VPC spoke needs to advertise the NAT subnet to the Network Connectivity Center hub. An export include policy is used to specify which routes (in this case, the 192.168.1.0/24 NAT subnet) should be advertised to the hub.

Global Dynamic Routing: To allow resources in us-west1, europe-central1, and asia-southeast1 to reach the on-premises location through the us-east4 Cloud Interconnect and NAT gateway, the VPC containing these resources (the spoke VPC) must have global dynamic routing enabled. This ensures that routes learned in one region (like the on-premises routes via us-east4) are available to VMs in all other regions of that VPC.

Options A and B configure Private NAT gateways in multiple regions, which consumes more IP addresses than necessary given that the Cloud Interconnect is only in us-east4. Option D uses 172.16.x.x for NAT subnets, which clashes with the on-premises IP range and the requirement to use the 192.168.0.0/20 space for cloud.

Exact Extract:

"Private NAT allows instances with private IP addresses in one VPC network to connect to on-premises or other cloud networks through a NAT IP address in a different region or network."

"To allow VMs in multiple regions to reach a central destination through a NAT gateway located in a specific region, you must configure global dynamic routing on the VPC network. This ensures that routes to the NAT gateway's subnet are propagated across all regions."

"When using Network Connectivity Center spokes, you can use export policies to control which routes are advertised from a spoke to the hub. An include policy specifies the exact prefixes to advertise."Reference: Google Cloud Private NAT Documentation, Network Connectivity Center Documentation - Spoke policies, VPC Network Documentation - Dynamic routing mode