Paul had explained how one man, Adam, sinned and brought death into the world. He then connected and finished his thought of verse 12 with verses 18-21.
Romans 5:12 (KJV)
Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
The new material:
Romans 5:18-21 (KJV)
Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life.
For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.
Moreover the law entered, that the offence might abound. But where sin abounded, grace did much more abound:
That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal life by Jesus Christ our Lord.
The first part of verse 18 is a repetition of verse 12. By the sin of Adam, the judgment of death came upon all mankind. The last part of verse 18 gives the comparison. In the same way, by the righteousness of Yeshua, the free gift of justification comes upon all mankind. Paul was describing how one man acted and how many received from the action without doing anything to deserve what was received. In other words, when Adam sinned, death came to all his descendants even though they had not done anything to deserve that punishment. (Remember, this is not saying that man does not suffer because of his own sin, but that the death penalty comes upon man before any sin is ever committed. The punishment is undeserved.) The same is true of Yeshua. By His righteousness, the gift of justification is available to all men even though they have done nothing to deserve it.
By Adam's disobedience many were made sinners (through the estrangement between God and man) (verse 19). In the same way, by Yeshua's obedience many shall be made righteous.
In verse 20, Paul reminded his readers that with the Torah, sin abounded. The amount of sinning was not more, but rather, the understanding of sin increased with the Torah, and man knew, not only by conscience but by Law, that he was committing sin. The accountability or guilt of sin increased. How much more, then, did grace abound by Yeshua's obedience? With the increased accountability for sin, God's gift of grace also expanded.
Sin reigns until man's death (verse 21). By contrast, grace reigns through righteousness unto eternity by Yeshua, the Messiah, our Lord!