“Can someone help me with this?”
You're trying to carry a big box from one office to another. It's a little too big for you to carry by yourself, so you ask for assistance.
Can someone help me with this?
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Can someone (do something)?
Make a request this way when you don't care who does it:
Can someone help me with this?
Can someone come down and take a look at my computer? It's acting up.
help (someone) with (something)
You can use this phrase to describe helping someone to do a certain activity.
I help my grandma with her garden.
He needs someone to help him with all these reports.
Notice that "garden" and "all these reports" are both noun phrases.