OK, i've been itching to give the answer to with Almita being so close!!!

The man would ask, " If i were to ask the other guard which door led to the execution room, which one would he say?" Whatever the answer was, he would go through. If he asked the lying guard, the lying guard would know that the other guard would tell the truth about which door was which, but he would then lie about it. If he asked the truthful one, this guard would know that the other guard would lie about which door was which, and so he would tell the truth about this. So, all in all, whichever guard says is the door to the execution room, is actually the door to freedom!

Hope you get that, it is complicated!!!