Hello In this sentence:

Meeting him for the first time , Charile was slightly nervous.

I understand that there are two caluses and that the subject is Charile the verb is "was" nervous is prediacate nominative and that "slightly" modifies nervous. In the other Clause, Meeting him for the first time, I think that "Meeting" is the verb "him" is the direct object and "for the first time" is a prepositional phrase modifying "Meeting". But, what does the whole clause "Meeting him for the first time" modify???

Thanks for your help! --
Prepositional Phrases can function as adjectives or adverbs.
Prep phrases used as adjectives come after the nouns they modify.
Prep phrases used as adverbs modify verbs or clauses. These prepositional phrases can come at different places in a sentence.

Meeting him for the first time , Charile was slightly nervous.
........................Prep phrase...................main clause.............

You are modifying the main clause......Charlie was slightly nervous
Well, for the first time is a prepositional phrase but Meeting him for the first time is not. It is a participle clause and functions as an adverb modifying the main clause, expressing the time relation between the two clauses. Because it functions as an adverb, it is also called Adverbial participle clause.

Participle clauses are very like relative clauses, except that they have participles instead of complete verbs. Compare:

Meeting him for the first time, Charlie was slightly nervous.
Charlie was slightly nervous when he met him for the first time.
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This is called an absolute. It is a participal phrase modifying the main clause, usu. called a sentence modifier.
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I know this is an old post but I would like to know how to diagram this sentence. I understand that the second sentence is modifying the first but I don't know how to join both.
Any help would be really appreciated.