2006I had finished cleaning the house when my aunt arrived.
Cleaning isn't a gerund, is it? Yes, it is the noun form of verb-ing. Cleaning the house is what you had finished.
Why do we use the "verb-ing" form in this sentence? What's the rule with this?
Because "cleaning" was what you had finished. "to clean" is not what you had finished.
Let's take another verb that would make it easier to understand the difference between 'verbing' and 'to verb'.
I stopped smoking my cigarette. This means that I was smoking my cigarette, but then the boss came in so I stopped smoking it.
I stopped to smoke my cigarette. This means I was doing something else, maybe working, but then I stopped working in order to be able to smoke my cigarette.
I stopped (working in order) to smoke my cigarette.
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