A developer is trying to install an application remotely that requires a graphical interface for...

The environment variable that must be set in remote shell in order to launch the graphical interface is $DISPLAY. This variable tells X11 applications where to display their windows on screen. It usually has the form hostname:displaynumber.screennumber, where hostname is the name of the computer running the X server, displaynumber is a unique identifier for an X display on that computer, and screennumber is an optional identifier for a screen within an X display. For example, localhost:0.0 means display number 0 on the local host. If the hostname is omitted, it defaults to the local host.

The other options are not correct environment variables for launching the graphical interface. $RHOST is a variable that stores the name of the remote host, but it is not used by X11 applications. SETENV is a command that sets environment variables in some shells, but it is not an environment variable itself. $SHELL is a variable that stores the name of the current shell, but it is not related to X11 forwarding. References: How to enable or disable X11 forwarding in an SSH server; How to Configure X11 Forwarding Using SSH In Linux