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Which part of speech is ' with problems ' ?

adjective phrase modifying people or adverbial phrase modifying help ?

Any comments ?
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If it's unclear from the context, use a pronoun.

"I help people with their English."

"I help people with their problems."

"I help people with my problems." (some kind of strange therapy?)
Comments  
It would seem to me to be modifying people.
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But " I help people with English " seems to be modifying help, right ?
 ryan smith's reply was promoted to an answer.
ThanksEmotion: smile

It sure clears the mess then. But normally the pronoun is understood. And people just skip it right ?
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I help people with problems

I help people with their problems

The ' with problems ' is adjective phrase whereas the ' with their problems ' is adverbial phrase I think.
If I rembember correctly, an adverbial phrase of instrument.