Question: How does Christ dying save anyone from anything?
Answer: That's an excellent question.
If a five-year old breaks a window, he might be sorry for having done it, but he certainly doesn't have the skills, nor can he earn the money, necessary to repair the window. As the child's father, I will have to repair the window.
But, as a good father, I won't do it by myself. I will require my child - the one who broke the window - to assist me. Perhaps he is only old enough to lift the glass up, perhaps even only able to lift it with my help. Perhaps I lift it, but he applies the putty around the edges. He might be required to hand me the tools as I do the repair. I don't do it alone, although I certainly could. He does as much work as he can, I complete what is too much for him. He really does work, but he really can't finish it without me.
When we sin, we break the world.
God made the world to be unbroken.
The world needs to be repaired.
Worse, a sin against God is a sin against infinite goodness, the source of life.
It is infinitely unjust, it is a rejection of Life Himself.
Such a rejection, in justice, deserves death, permanent separation from God.
In mercy, we can forgive, but in justice, that evil, that brokenness, demands healing. It demands that SOMEONE undertake the work necessary to repair the injustice for the evil that was done. This work is commonly called "punishment"
Fortunately for us, God is perfect justice AND He is perfect mercy.
God does not desire us to be separated from Him at all, much less permanently.He recognizes that we may be remorseful for our sins, but He also knows we are unable to handle the punishment for our sins. So, He takes the bulk of the punishment on Himself. We still suffer for our sins, but He suffers with us, shouldering the greatest portions of the burden. That's why Christ's dying can save anyone from anything. Whatever you've done, if you are truly remorseful, God has volunteered to take on the full work necessary to repair our injustices, even unto death.