It is possible to hide an application (and it's open windows) by selecting "Hide [appname]" from "the application menu" in the menu bar. The application menu is the right-most menu, to the right of the help menu, and is always present.
However, it may be desirable to script the hiding of an application. The following AppleScript can be used in various situations to aid in this automation. In FileMaker Pro, this can be used in a "Perform AppleScript" step in a ScriptMaker script.
tell application "Finder"
set visible of process "FileMaker Pro" to false
end tell