On an ABC Browse window, what is the event/embed used to capture a double-click of the mouse?

If you mean in the list box you can alert(MouseLeft2) and then in EVENT:AlertKey check for KeyCode() = MouseLeft2

! ABC Objects -> Browse on File... -> TakeKey [4500] 

CASE KEYCODE() 
OF MouseLeft2 
   SetKeyCode(0) !Here you clear the pressed key
   POST(Event:Selected,?List) 
END

There are many ways that lead to Rome.
In the Control Events of the Browse:

This way you can also test (if necessary) in what column the user clicked.

OF EVENT:AlertKey
  ! Start of "Control Event Handling"
  ! [Priority 4499]
  IF KEYCODE()=MouseLeft2
    IF ?Browse:1{PROPLIST:MouseDownRow}>0         !double left mouse in list
      IF ?Browse:1{PROPLIST:MouseDownField}=4      !click in column 4