Why did Adam and Eve not die after eating from the tree of the knowledge of good and evil? I just began reading the Bible.

In Genesis 2, it says


  And Jehovah God commanded the man, saying, Of every tree of the garden
  thou mayest freely eat: but of the tree of the knowledge of good and
  evil, thou shalt not eat of it: for in the day that thou eatest thereof
  thou shalt surely die.


Why did they, ultimately, not die? Instead, God punishes them in some other way.
Adam and Eve Suffered Spiritual Death

The death of which God spoke, "on the day that thou eatest thereof," was the spiritual death of Adam and Eve. (Physical) Death entered the world by that act, too (Romans 5:12). Before they had rebelled against God, there was no death, in any form. But to make sense of God's command, it makes more sense (to me) for him to be speaking of spiritual death.

Perhaps one could say that this is not the death of which God appears to be speaking, but which death is more serious, the death of the body or the second death (Revelation 20:14)?

If we assume that the Scripture is true and consistent, then it is not unreasonable to conclude that God was not speaking of their immediate physical death, since death clearly entered the world on that day, and both Adam and Eve earned spiritual death (Romans 3:23).