Why is sentence #1 correct and not sentence #2? 1. Did your hear about my breaking my toe? 2. Did you hear me breaking my toe?
My indicates possession and the act of breaking your toe is possessive. You essentially own the act! It is much the same as if you were to say: "Did you here about my new car!" - You won the car, thus you possess the action of breaking your toe in the same way.
That is the simple answer, but pronoun usage remains difficult for many students because they are used to hearing pronouns used incorrectly. Here are a couple of excellent sites that will help you to better understand pronoun case and pronoun usage:
The second link has a wealth of other useful information regarding both writing and grammar. Bookmark it now as you may find it useful again in the future!