Okay, you didn't ask about the first time God answered one of my prayers, but I'm going to tell you anyway.
I was maybe three or four years old. One day I was playing with what my mom used to call "the bell." It was one of those little portable timers people use when they're cooking (nowadays they're generally built-in, but this was a long time ago, and ours wasn't). Anway, I was sitting and winding it just past the 5-minute mark and then immediately backwards to where it would go, "ding!" So it was wind clockwise, wind counter-clockwise, ding! Wind clockwise, wind counter-clockwise, ding! Over and over and over again. Finally my mother said to me, "Kathryn, don't do that any more. You're going to end up breaking it. It's not supposed to be a toy." Well, since I was so much smarter than she was, I just answered, "No I'm not! See!" and I continued to go through my little routine. A few more winds, a few more dings and all of a sudden, the bell stopped working. Guility, I handed it to my mother. "Im sorry," I said. She tried for a few minutes to get it to work. Finally, she said, "Well, I told you that's what would happen, but you didn't listen to me, did you. We'll just have to buy a new one." "No we won't!" I said. "I'll pray about it. I'll ask Heavenly Father to make it work again." My mother really didn't know what to do. She'd taught me to pray and to have faith that God would hear and answer my prayers, but she knew that He didn't waste His time fixing mechanical timers. She hesitated and started to try to discourage me, but I was determined. "I'm going to pray!" I said. And I did. After I asked God to please fix the bell, I went over and picked it up. I wound it just past the 5-minute mark and then backwards. DING! What a beautiful sound! I handed "the bell" to my mother, who was standing there were her mouth open. Do I believe God answered my prayer? Absolutely. Would I have that much faith today? Probably not. But I believe God knew how important it was that He answer that prayer. He knew it would influence the way I thought of him forever.