Yes, of course he could. God can do *anything* including this.....oh, wait. That would mean you *couldn't* lift the rock so, like, that would mean he wasn't all powerful (which he is). I'll change my answer then. God coulnd;t make a rock this big becasue he could move *any* rock. Aw, darn it. That would mean he wasn;t capable if creating this object when clearly he could do anything!
Wow - you got me! This is a REALLY BIG QUESTION and your teacher is very smart to ask it!
(sarcasm off)
The answer is that it is a pardox. Might as well ask "can god make a white ball that is totally black?". It's a pardox. The two cannot exist together. Could God make you exists and not-exists at the same time? No.
And your question hasn't set any parameters for God either so I could actually also answer it as simply "No, God doesn't have the power to do this" Odin wasn't all powerful, so he couldn't have done this either. Was this the God you were talking about?