The man closed his mouth and scratched his cheek.
The man had closed his mouth and scratched his cheek.
It is even possible to express in that way? Using the possession word "had"? And when might it be necessary to do so?
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Sign up to join this community"had" here indicates that the event happened before the moment in the past being described in the sentence, i.e in the past perfect tense, not as a possessive. The verb to have (Has/have/had) serves two different functions, as a possessive to indicate that a person/thing owns something or possesses a certain characteristic, and to form the perfect tenses.
In this case, "had" does not function as a possessive, but rater as a part of the Past Perfect tense. Therefore, the question basically boils down to "when to use Past Perfect vs. Past Simple", and I'm sure you'll be able to find the answer to that in any grammar reference.