Hello:
You need to set the rule on the field that is going to change. Given your example, you'd add the rule to the field that is bound to the Doors dropdown list. The rule would have an action to set a field's value. The field would be the DoorChangeDate field. Select the fx button next to the area where you can enter the value, and enter today() for your formula.
I'd make the DoorChangeDate field a date data type rather than a string. You can do this by right clicking the field in the Main Data Source in the Data Source Task Pane. Change it from Text to Date.
As an aside, in case you weren't aware of this, you don't need to display the field on the form if you don't want to. The field will still have the data value you've set.