Hi Guy,
CustomerEquipment is a table from the Field Services app (available with Method CRM Pro only), do you have this app installed? If you have a Pro account, you can install the Field Services app through Customize > My Account. Please see http://www.methodintegration.com/method/kb.aspx?folder=methodcrm&article=Field-Services-Overview&id=222 for more details.
If you have it installed, I'll walk you through the process. Please edit the Activity table by going to Customize > Tables/Fields > Activity. Select "Add a Linked Field", Link Using CustomerEquipment, and then select the linked field you would like to display (for example Name). Then to add the field to a screen, you would drag the new field onto a section while editing the screen.
If you have questions about any of this please let me know.
-Russell