The Christian (we'll just call him Christian) he was talking to went over the facts of the Gospel and the young man said he was prepared to yield to Jesus Christ as Lord. Christian asked him to imagine standing at heaven's door and God saying, "Why should I let you in?" What would his answer be? He said that he was going to try from now on to do good works so hopefully he should be able to do enough before arriving at heaven's door. Christian explained to him that he had absolutely no hope of entering heaven on that basis. God is absolute in His righteousness and demands good works all the time, so presenting good works does not absolve us from the guilt of our sin. Those sins must be answered for and the penalty paid.
He then tentatively asked if acknowledging his sin might get him in. Christian told him he ought to acknowledge his sin and be sorry for it, but that doesn't pay for them. If someone was not sorry for his sin then that would only be an additional sin to add to the others, so just being sorry for our sins won't save us from the punishment they deserve.
At this point he was at a loss, so Christian went over in more detail what Christ did at the cross, using the words of Isaiah 53 v 5:
But He was wounded for our transgressions, He was bruised for our iniquities...And Christian explained that the Lord was there taking what we deserved, He was suffering as a substitute. At this point his eyes widened and he said, "Ah! He took the punishment so I don't have to! That makes it so clear. That's a weight off my shoulders. That's it! And He's done it, that will never change, that's it forever!"
Christian brought him back to heaven's door and God is asking why he should be let in, what's the answer now? "Because Jesus died for me" was his response.
And that's the right answer, and the only right answer. If you can find someone else who has paid for your sins then by all means trust that person, but no one else has, no one else could, and that is why the only hope for sinners like us is in the Son of God who loved us and gave Himself for us (Galatians 2 v 20).
That's it.