Is the VPN gateway 1 hop behind the firewall gateway? Or is it parallel, with the VPN gateway's external interface sharing the same subnet as the firewall gateway? Your network addressing makes it look parallel. Your diagram also suggests the VPN gateway's internal interface has to pass traffic back through the firewall gateway on another interface (which is fine).
In addition to the message from PhoneBoy (check his suggestion first), this also sounds like you are missing a return route on the firewall gateway for the office mode subnet (172.10.0/22). I suspect your firewall gateway, or perhaps the VPN gateway, is performing NAT and you aren't expecting it. The firewall gateway will see source IP packets of 172.10.0.0/22, so they need to be returned to the VPN gateway. You can see this with fw monitor. You can run this command on both gateways, which will give you a hint:
fw monitor -F 172.20.1.2,0,0,0,0 -F 0,0,172.20.1.2,0,0
You can also check your logs and you will see if NAT is being applied.
Similarly, make sure your interior network (10.10.6.0/24) has either a default route, or some type of route, to also send packets for 172.20.0.0/22 back to the firewall gateway.