The first of the "two new commandments" are direct relationship to the first four of the ten commandments, how to love GOD,
Jesus said
John 14:15
If ye
love me, keep my commandments.
Which the nation of Israel did not do.
The second of the "two new commandments" are direct relationship to the last six of the ten commandments, how to love your neighbor
The reason they were new because the Israel nation were not keeping the law according to GOD so to the Israel nation they were "NEW"
Jeremiah 31:32-34 King James Version (KJV)
32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the Lord:
33 But this shall be the covenant that I will make with the house of Israel;
After those days, saith the Lord, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
(this says "after those days" not at birth so Adam and Eve did not have it written on their hearts at birth)
34 And they shall teach no more every man his neighbor, and every man his brother, saying, Know the Lord: for they shall all know me, from the least of them unto the greatest of them, saith the Lord: for I will forgive their iniquity, and I will remember their sin no more.
Hebrews 13:8 [Full Chapter]
Jesus Christ the same
yesterday, and to day, and for ever.