What is the firewall type that allows packets matching a known active connection to pass through?

The correct answer to the following question will be "Stateful firewall ".

Explanation:

A network firewall that monitors the state of service and the qualities of wireless networks that traverse it, termed as Stateful firewall. The firewall is designed to identify valid network packets for the various link types. It's a form of firewall that allows the passage of packets that suit a known active link.The network admin can set the conditions in a firewall that utilizes stateful inspection to meet certain criteria. Ports are shut in a standard network unless a received packet requests access to a specific port and only that port is unlocked.

Therefore, a Stateful firewall is the right answer.