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I know that simple words that end with "ly" are adverbs. "She sings nicely". Before, I thought that everything that indicates "why?where?when?how?" is an adverb. But now I realized they can be adjectives, when they are part of an adjectical phrase.

"I bought a shirt for you"
Initially, I thought that "for you" was the reason why the shirt is bought. But later, I found out that "for you" is an adverb complement that is part of an omitted adjectical phrase. Therefore, it's an adjective. "I bought a shirt that is for you.

Now, I began to think that every adverbial that follows an object is describing the object and not the verb!

"I played volleyball on the beach"
"on the beach" easily modifies where you played, but I can also phrase it as "I played volleyball that is on the beach" or "Which kind of of volleyball? The on the beach kind?" Although, they don't make logical sense, they still can work as an adjectival!

My main problem is that, how do I distinguish an adverb or adjective, when these words are placed after the object?
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Judging from your comments and examples, I can recommend nothing more specific than common sense. 'On the beach' reasonably indicates where the game was played, so it is a sentential adverb of place.
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BlackBlitzI began to think that every adverbial that follows an object is describing the object and not the verb!
No! You don't want to do that!
BlackBlitz"I played volleyball on the beach"
"on the beach" easily modifies where you played, but I can also phrase it as "I played volleyball that is on the beach" or "Which kind of of volleyball? The on the beach kind?" Although, they don't make logical sense, they still can work as an adjectival!
Actually, it's because they don't make logical sense that they can't work as adjectival in this sentence.

I can't see the volleyball on the beach, but I can see the volleyball in the car.

Here on the beach and in the car are adjectival -- not because they tell which kind of volleyball, but because they tell which volleyball.

CJ