How do I install the 7847i internet communicator to my Vista 15P Control Panel?

You follow the same steps as you would if installing the 7847i to a Vista 20P.

First, open the 7847i enclosure by pushing in the tabs located at the bottom of the device. Turn off the control panel by disconnecting the AC transformer and one back-up battery lead. Now connect the 7847i to your Vista 15P control panel using four-conductor wire.

Connect the:

7847i's 3rd terminal to the control panel's 5th terminal.
7847i's 4th terminal to the control panel's 4th terminal.
7847i's 5th terminal to the control panel's 7th terminal.
7847i's 6th terminal to the control panel's 6th terminal.

Use screws and anchors to mount the unit to the wall. Insert an Ethernet cable into the device and connect the other end to your router. Shut the 7847i enclosure and reconnect power to the Vista 15P control panel.