What is the difference between these sentences, and their particle usage?
- watashi wa kore ga sukidesu
- watashi ga kore o sukidesu
I don't really understand the usage of these particles.
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Watashi wa kore ga sukidesu.
... is neutral and very basic "I like it". It's the most basic way to say "I like ～" in Japanese. See: 私は猫が好き and 猫は私が好き
Watashi ga kore ga sukidesu.
This sentence uses exhaustive-listing ga described here. When someones asks "Who likes it (among those people)?" then this sentence would be the natural response. It's like saying "I like it" with emphasis on "I".
Watashi ga kore o sukidesu.
This is semantically the same as Sentence 2. In complex sentences, sometimes を can be used instead of が as if 好き were a normal verb. This phenomenon has been discussed several times on this site (see: Why is を used in this situation? 私は先生がネコを好きだと思います and Usage of ～を好き outside of embedded clauses ). In your example, instead of saying が twice, you can replace the second が with を. According to this article (in Japanese) this happens more often in younger generations. But I think this one is grammatically exceptional, so I recommend you familiarize yourself with Sentences 1 and 2 first.