The most cost-effective architecture for deploying third-party firewall appliances for traffic inspection and NAT capabilities in a VPC, with the requirement to deploy these appliances behind a load balancer, involves using a Gateway Load Balancer (GWLB). The GWLB is specifically designed for deploying, scaling, and managing virtual appliances, such as firewalls, in the cloud. It simplifies the deployment and scaling of third-party virtual appliances by providing a single point of entry and exit for traffic that needs to be inspected. Option A is the correct choice because it suggests deploying a Gateway Load Balancer with the firewall appliances as targets, configuring the firewall appliances with a single network interface in a private subnet, and using a NAT gateway to send the traffic to the internet after inspection. This approach is cost-effective as it leverages the GWLB's capabilities to efficiently manage traffic to the firewall appliances without the need for additional network interfaces or complex configurations. It also utilizes a NAT gateway for internet-bound traffic, which is a managed service that simplifies NAT operations and reduces the operational overhead compared to configuring NAT on the firewall appliances themselves.