I'd prefer it with "your": "your coming down here" = "the fact that you've come down here".
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NaOH" we really appreciate you coming down here." i kind of have a feeling that instead of using 'you' we can use 'your' as well. a quick remark on the sentence structure will also be very helpful.In this sentence, the gerund 'coming' is used as a noun and requires a possessive adjective, 'your'.