The Lord pointed out to the Nephites while he was teaching them face to face that the Gentiles would find God's favor because of their "belief" in Him. Interestingly, the Lord says it is because of the belief of the Gentiles, but also the "unbelief" of the house of Israel, that the truth would come unto the Gentiles in the latter day.
"blessed are the Gentiles, because of their belief in me, in and of the Holy Ghost, which witnesses unto them of me and of the Father. Behold, because of their (the Gentiles) belief in me, saith the Father, and because of the unbelief of you, O house of Israel, in the latter day shall the truth come unto the Gentiles, that the fulness of these things shall be made known unto them." (3Nephi 16: 6-7)
The "fullness of these things" refers to all the Lord made known to the Nephites and allowed them to write during His ministry among them. The Book of Mormon contains the fullness of the gospel of Jesus Christ. All that is needed for every person to learn what is required to "come unto (Him)" can be learned from the words of the Book of Mormon. It is that fullness, the Gentiles are promised to receive in the latter day.
Centuries earlier, in Nephi's day, the angel of the Lord said "if the Gentiles shall hearken unto the Lamb of God in that day that he shall manifest himself unto them in word, and also in power, in very deed..." (1Nephi 14: 1) The manifestation of the Lord "in very deed" is the culminating blessing of the fullness of Christ's gospel. That manifestation comes to every person who is willing to believe in Him and obey the narrow and strait course laid out by the Lord for the return to Him. The course back to His presence and the reception of His promises from His own mouth are available to every person who is willing. Joseph Smith the latter day Gentile prophet of restoration taught these principles and invited every latter day saint to "make their calling and election sure." The best source of which I am aware (in addition to the Book of Mormon and the scriptures,) to learn about the path and the requirements that must be met in order to receive such a manifestation from the Lord, is The Second Comforter Conversing With the Lord Through the Veil by Denver C. Snuffer Jr. After a person has immersed herself completely and feasted fully and regularly on the words of the Book of Mormon and the scriptures, then a careful reading of the Second Comforter can open wonderful understanding and helpful instruction for the sincere seeker.
The entirety of the restoration work of Joseph Smith, the bringing forth of the Book of Mormon and other latter day scripture, constitutes fulfillment of the Lord's words, "in the latter day shall the truth come unto the Gentiles, that the fullness of these things shall be made known unto them." (3Nephi 16: 7)
Through Joseph Smith, the latter day Gentiles received the "fullness of these things." They were offered the opportunity to become Zion. They might have been of one heart and to have had no poor among them. They received the invitation to have the Lord dwell among them in a house to be built unto His name. The latter day Gentiles instead, began early on in their history to fulfill the further words of the Lord and the prophets of the Book of Mormon. Those further words and prophecies do not flatter the latter day Gentiles (as we have seen in the final two verses of 3Nephi.) The favor and blessing of God enjoyed by the Gentiles through the period of restoration of truth is replaced with warnings and pronouncement of woes upon them.
Immediately after the pronouncement of the Lord to the Nephites that "in the latter day shall the truth come unto the Gentiles, that the fullness of these things shall be made known unto them;" in the next verse the Lord begins to pronounce woes upon them. The next recorded words in the Nephite record begin with this, "But wo, saith the Father, unto the unbelieving of the Gentiles..." (3Nephi 16: 8) The Lord then prophesies to the Nephites about the failure of the latter day Gentiles and the removal of the fullness of the gospel from them.
"And thus commandeth the Father that I should say unto you: At that day when the Gentiles shall sin against my gospel, and shall reject the fulness of my gospel, and shall be lifted up in the pride of their hearts above all nations, and above all the people of the whole earth, and shall be filled with all manner of lyings, and of deceits, and of mischiefs, and all manner of hypocrisy, and murders, and priestcrafts, and whoredoms, and of secret abominations; and if they shall do all those things, and shall reject the fulness of my gospel, behold, saith the Father, I will bring the fulness of my gospel from among them. (3Nephi16: 10)
The Lord's prophecy includes the following infractions of God's law by the latter day Gentiles. They will:
1. Sin against my gospel
2. Reject the fullness of my gospel
3. Lifted up in the pride of their hearts
4. Filled with all manner of lyings, deceits, mischiefs, hypocrisy, murders, priestcrafts, whoredoms, secret abominations
The result for the Gentiles is a pronouncement by the Father, "I will bring the fulness of my gospel from among them." (See D&C 45: 28-30) The favor of God enjoyed by the Gentiles through the period of restoration of truth by the prophet Joseph Smith is to be removed from them. Then, in the great chiasmic arrangement of stewardship responsibility for the gospel of Jesus Christ throughout the ages of the earth since Christ, those that were first shall now be the last to receive the fullness of the gospel. The favor of the Lord will shift from the Gentiles to the remnant and all of Israel.
"And then will I remember my covenant which I have made unto my people, O house of Israel, and I will bring my gospel unto them. And I will show unto thee, O house of Israel, that the Gentiles shall not have power over you; but I will remember my covenant unto you, O house of Israel, and ye shall come unto the knowledge of the fulness of my gospel." (3Nephi 16: 11)
Given the context and understanding of what we have learned from the precious Book of Mormon about the latter day Gentiles, it seems less surprising now that the Lord would instruct Mormon to insert these words as the final words of the book 3Nephi:
"Turn, all ye Gentiles, from your wicked ways; and repent of your evil doings, of your lyings and deceivings, and of your whoredoms, and of your secret abominations, and your idolatries, and of your murders, and your priestcrafts, and your envyings, and your strifes, and from all your wickedness and abominations, and come unto me, and be baptized in my name, that ye may receive a remission of your sins, and be filled with the Holy Ghost, that ye may be numbered with my people who are of the house of Israel." (3Nephi 30: 2)