Rom 6:12
Reign (βασιλευέτω)
The antithesis implied is not between reigning and existing, but between reigning and being deposed. (Dr. Marvin Vincent

Rom 6:12 Let not sin reign even in your mortal body - It must be subject to death, but it need not be subject to sin. (John Wesley)

Rom 6:11
Reckon ye also yourselves to be dead - Die as truly unto sin, as he died for sin. Live as truly unto God, as he lives with God. This seems to be the spirit of the apostle’s meaning. (Dr. Adam Clarke)

Rom 6:10 He died to sin - To atone for and abolish it. He liveth unto God - A glorious eternal life, such as we shall live also. (John Wesley)

This is certain because, Christ being raised from the dead, dieth no more. He now lives eternally, and we who are in him, having shared his death, must share his eternal life.  (The People's New Testament)

We be dead (ἀπεθάνομεν)
The aorist. Rev., correctly, we died. The death is viewed as an event, not as a state. (Dr. Marvin Vincent)

For he that is dead is freed from sin.  When a slave died he was freed from his master's service; so when one has died to sin, he is no longer the slave of sin, and is freed from his service.  His power over the bodily members should be destroyed. (The Peoples New Testament, 1891)

Knowing this - We all knowing this.  All Christians are supposed to know this.  This is a new illustration drawn from the fact that by his crucifixion our corrupt nature has been crucified also, or put to death; and that thus we should be free from the servitude of sin. (Dr. Albert Barnes)

Rom 6:5 For - Surely these two must go together; so that if we are indeed made conformable to his death, we shall also know the power of his resurrection. (John Wesley)

Rom 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead (d) by the glory of the Father, even so (e) we also should walk in newness of life.

(d) So that Christ himself, being released of his infirmity and weakness, might live in glory with God forever.

(e) And we who are his members rise for this purpose, that being made partakers of the very same power, we should begin to lead a new life, as though we were already in heaven.  (Geneva Bible Translation Notes)

Baptized into his death? - That, as Jesus Christ in his crucifixion died completely, so that no spark of the natural or animal life remained in his body, so those who profess his religion should be so completely separated and saved from sin, that they have no more connection with it, nor any more influence from it, than a dead man has with or from his departed spirit. (Dr. John Gill)

Dead to sin - Freed both from the guilt and from the power of it. (John Wesley)

Rom 6:1 The apostle here sets himself more fully to vindicate his doctrine from the consequence above suggested, Romans 3:7-8. He had then only in strong terms denied and renounced it:  here he removes the very foundation thereof.  (John Wesley)

Rom 5:21
That - even so grace might reign (hinȧ̇houtos kai hē charis basileusēi). Final hina here, the purpose of God and the goal for us through Christ. Lightfoot notes the force of the aorist indicative (ebasileusen, established its throne) and the aorist subjunctive (basileusēi, might establish its throne), the ingressive aorist both times. “This full rhetorical close has almost the value of a doxology” (Denney). (Robertson's Word Pictures)

A preventing of an objection: why then did the law of Moses then enter?  So that men might be so much more the guilty, and the benefit of God in Christ Jesus be all the more glorious.  (a) In addition to that disease which all men were infected with by being defiled with one man's sin, the law entered.  (b) Grace was poured so plentifully from heaven that it did not only counterbalance sin, but beyond this it surpassed it.  (Geneva Bible Translation Notes)

The foundation of this whole comparison is this, that these two men are set as two heads or roots, so that out of the one comes sin by nature, and from the other righteousness by grace springs forth upon others.  So then, sin enters not into us only by following the steps of our forefathers, but we receive corruption from him by inheritance. (Geneva Bible Translation Notes)

Rom 5:18:  Justification of life - Is that sentence of God, by which a sinner under sentence of death is adjudged to life. (John Wesley)

The emphatic point of the comparison.  The effect of the second Adam cannot fall behind that of the first. If death reigned, there must be a reign of life. (Dr. Marvin R. Vincent, Vincent's Word Studies)

The sentence was by one offence to Adam's condemnation — Occasioning the sentence of death to pass upon him, which, by consequence, overwhelmed his posterity.  But the free gift is of many offences unto justification - Unto the purchasing it for all men, notwithstanding many offences. (John Wesley)