Would you explain more clearly when one does or does not use "de" in this form? As far as I can extrapolate, if an infinitive is to follow, we use "de" but otherwise no?
Or is it optional in any instance?
In the lesson, after the boxes containing examples, some using the preposition de and some without it, we say: "As you can see from the previous examples, when we use deber with this nuance of assumption/wondering, we can optionally use the preposition "de" after deber."
This lesson is about how to say "something must have happened"; this is talking about assumption, not obligation. So for all the examples in this lesson "de" is optional.
To see with more detail the difference between deber and deber de, please have a look at this other lesson which explains precisely this. There is a link at the bottom of the lesson about "something must have happened". Here it it.
I hope it is useful.
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