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As a rule, use the possessive case before a gerund, that is,a verb used as a noun. Gerunds are formed by adding -ing to a verb stems: going, eating, writing, borrowing. Like nouns, they are used as both subjects and objects. Take these examples similar to yours.
1. I don't like my brother's borrowing so much money.
2. I don't his eating so much ice cream.
3. I don't approve of his driving with such worn-out tires.
4. I recommend his seeing a doctor.
In these sentences, borrowing, eating,driving, and seeing are gerunds, preceded by possessive forms. If the first sentence had said brother rather than brother's , it would seem to say I don't like my brother rather than I don't like his borrowing so much. Similarly, if sentence 2,3, or 4 had used him instead of his, the meaning of the sentences would be changed. If an exam question offers you a choice between a possessive and an objective pronoun before a gerund, look carefully at what the sentence is saying. It is likely that the possessive is the better choice.
Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...