DON'T allow remote gui rpc until you've understood what is going on and why.
Read Controlling BOINC remotely for the background behind what the terms mean. 'Remote' in this case usually means another computer in your home or workplace: the processes don't work well over wider area networks, and in any event external computers should be blocked by your firewall or router. Of course, in this day and age, close-by computers can possibly hack into your WiFi, but let's assume not for the time being...
In normal usage, the BOINC client and the BOINC Manager both run on your local computer, and communicate with each other over a connection known as 'localhost' or IP address 127.0.0.1
It is possible to manage the BOINC client on one machine from a Manager (or replacement like the BoincTasks that's been mentioned already) on another machine: in that case, you have to authorise the process to use remote gui rpcs. This is usually described in terms of "The remote computer's IP address", but that's not strictly true: IP addresses are assigned separately to each network interface, so it's possible for a single computer to have two or three IP addresses (cable, WiFi, VPN to employer, would all be different). That might confuse things.
Also, I see you have 4 computers attached to this project. Maybe you (or a colleague) have set up remote control already, but a change in the network has moved one of the machines out of the permitted range of IP addresses. You need to have a sniff around your local network (whatever that means in your environment) and find out who's doing what, before you open the doors to every passer-by.