What is the basis within God that enables Him to forgive sin, is it on the basis of His mercy or on the basis of His justice?

Mercy is that attribute of God by which He withholds from us judgment that we deserve. Jeremiah puts the concept into perspective in Lamentations 3:22It is of the LORD's mercies that we are not consumed, because his compassions fail not.
See All... - "It is of the LORD'S mercies that we are not consumed." As such, we can say that God's mercy gives us time to be saved. We could even say that His mercy motivated Him to find a way of salvation for us. However, salvation requires a divinely legal solution. Salvation must satisfy the righteous requirements of God's justice.

Central to God's character is His holiness. On two occasions (Isaiah 6:3And one cried unto another, and said, Holy, holy, holy, is the LORD of hosts: the whole earth is full of his glory.
See All...; Revelation 4:8And the four beasts had each of them six wings about him; and they were full of eyes within: and they rest not day and night, saying, Holy, holy, holy, LORD God Almighty, which was, and is, and is to come.
See All...) we read of the heavenly beings crying out, "Holy, holy, holy." This is the only attribute of God that is so proclaimed. God's primary trait is His holiness. Yet, holiness demands justice. And justice requires that sin must be punished. The problem with salvation is how to take unholy men to a heaven that cannot allow anything defiled to enter its holy environs (Revelation 21:27And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.
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In order to solve this dilemma, much of our salvation takes on a legal character. Justification and propitiation are legal terms. Imputation is a legal act. The justice of God must be satisfied. I will try to explain what I mean by defining these terms.

Justification is the act by which I am declared just in the eyes of God. Without justification, I cannot enter heaven. But I cannot be declared just on the basis of my own holiness, for all have sinned and come short of the glory of God (Romans 3:23For all have sinned, and come short of the glory of God;
See All...). I am a sinner and that sin has to be paid for. Justice must be served. But for me to pay for my own sins would mean my eternal suffering in hell. This is where imputation comes into play.

Imputation is a double act. By imputation, my sin is placed on Jesus by way of His sufferings on the cross and the righteousness of Christ is imputed or applied to me by the same act. "For he [God the Father] hath made him [Jesus Christ] to be sin for us, who knew no sin; that we might be made the righteousness of God in him" (2 Corinthians 5:21For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
See All...). It is this trade through imputation that makes the way for us to enter heaven. We do not go in our own righteousness, but in the righteousness of Jesus Christ. Listen to Paul's desire: "And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith" (Philippians 3:9Thy bow was made quite naked, according to the oaths of the tribes, even thy word. Selah. Thou didst cleave the earth with rivers.
See All...). But how did Christ do away with my sins? That is the work of propitiation.

Propitiation is that act of salvation by which the wrath of God against sin is satisfied. For justice to be served, sin must be punished with the wrath of God. On the cross, Jesus became sin. The Father then turned His back on the Son (seen by the darkness on the earth) and He unleashed His full fury against the Son. Jesus suffered this wrath for the sake of those who would come under the redemption of His blood. The Father accepted this payment as fulfilling His requirement for justice. Isaiah 53:11He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities.
See All... prophesied, "He shall see of the travail of his soul, and shall be satisfied." That is, God would see the suffering of His Son for sin and would be satisfied that justice had been fulfilled for those who would trust in His Son for salvation. My sin is done away with through the sufferings of Christ on the cross. Christ has satisfied the Father and we are accepted in Him (Ephesians 1:6To the praise of the glory of his grace, wherein he hath made us accepted in the beloved.
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This is holy ground on which we walk. I always glory in God's goodness when I think of such things.