This is a good question; obviously everyone thinks they know the answer but don't understand the grammar. "Your" is grammatically correct because "walking" is a verbal noun (gerund) and requires a possessive pronoun. However, this rule has been ignored for so long that the personal pronoun "you" has gained practical acceptance and the only time this will ever matter in real life is on an Oxford placement test. Given the choice, "your" is more technically correct. This is an academic explanation of current thinking on which pronoun is preferred, from a grammar and linguistic point of view: http://www.oxfordreference.com/view/10.1093/acref/9780199661350.001.0001/acref-9780199661350-e-4464

Hi! It's correct saying: I won't you walking home all by yourself (I don't want that you walk home alone) / I won't have you walking home all by yourself (I will not let you walking home alone). You = noun/pronoun Your = possessive adjective Hope this help. Noemi

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Hi! Many thanks!