Unfortunately, Adam did that one thing that God had warned would bring death. When we think of the death that Adam's sin brought, we most often think of the physical element of that death. However, since Adam was a triune being, made up of spirit, soul, and body, we must realize that his death affected every part of his existence. As we apply our definition of death to the various parts of Adam, we see just how extensive the penalty for sin really was. Remember our definition for death.
Death is when someone or something ceases to function for the purpose for which it was created.
Adam's spirit was created to allow him to know God, to have an intelligent understanding of God. After the fall, Adam's spirit knew not just God, but it came to know good and evil. So we see that Adam's spirit, which was created to know God, came to know good and evil. It was no longer functioning for the purpose for which it was created. Adam's soul was the center of his will and emotion and was created to allow him to be a friend of God.