When I was first asked this question, I didn't know how to respond. It took me by surprise and I needed to ask the Lord what to make of it. The point of the question is to trick you into saying that God can't do something, when the God we worship is capable of anything. So, if your answer to the question is "Yes, He can make a rock so heavy that he can't lift it," then you're saying He can't lift the rock, therefore He isn't as capable as we praise Him to be. If your answer is "No, God can't make a rock so heavy that he can't lift it," then you're still saying He can't.
I couldn't wrap my head around the question, but then God reminded me of my initial responses. When my friend kept insisting that I give him a solid answer, the only thing I really could say is, "God wouldn't do that." He kept on, "I'm not asking if He would. I am asking if He can."
The thing is, everything in creation is possible because God would. He would, so He did. A huge reason why the question is so confusing is because it doesn't make sense. It's absurd -- a twist on words. Everything we know and understand in this world is because God gave us the ability to know and understand things that He made to exist for His glory. There's nothing we know that He doesn't already know. Since God would not make a rock so heavy that He Himself could not lift, it doesn't exist. Even the phrase itself is mind boggling because of its uselessness to God's glory and its inexistence.
The bottom line is that if God wouldn't do it, it doesn't exist. Should you ever find yourself in the same position, just say that phrase.
