In Romans 5:20 We are told "moreover, the Law entered that the offense might abound.:"

In the earlier verses we learn that by one man's offense death reigned. Also by one man sin entered into the world and death by sin and so death pass upon all men. We all know who that one man is. 

But Adam's offense was not the only offense. The free gift was for many offenses. The Bible says death reigned from Adam to Moses even upon those who did not sin after the similitude of Adam's transgression. Even upon man who did not sin like Adam did, death reigned.

The simlitude of Adam's Transgression

You did not have to sin like Adam to be a sinner, Or for death to reign over you, Adam's sin was a deliberate disobedience to God;s Law. 

Take a man like Lamech, In Gen. 4:23 he said And Lamech said unto his wives, Adah and Zillah, Hear my voice; ye wives of Lamech, hearken unto my speech: for I have slain a man to my wounding, and a young man to my hurt. 

Sin multiplied on the face of the earth and it hurt God immensely but in this pre-law condition it was left to their conscience to tell them this was wrong. ​

11 The earth also was corrupt before God, and the earth was filled with violence.

12 And God looked upon the earth, and, behold, it was corrupt; for all flesh had corrupted his way upon the earth.

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Then the Law entered that the offense might abound,

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