14 Verily, verily, I say unto thee, blessed art thou for what thou hast done; for thou hast inquired of me, and behold, as often as thou hast inquired thou hast received instruction of my Spirit. If it had not been so, thou wouldst not have come to the place where thou art at this time.
15 Behold, thou knowest that thou hast inquired of me and I did enlighten thy mind; and now I tell thee these things that thou mayest know that thou hast been enlightened by the Spirit of truth;
16 Yea, I tell thee, that thou mayest know that there is none else save God that knowest thy thoughts and the intents of thy heart.
17 I tell thee these things as a witness unto thee--that the words or the work which thou hast been writing are true.
18 Therefore be diligent; stand by my servant Joseph, faithfully, in whatsoever difficult circumstances he may be for the word's sake.
19 Admonish him in his faults, and also receive admonition of him. Be patient; be sober; be temperate; have patience, faith, hope and charity.
20 Behold, thou art Oliver, and I have spoken unto thee because of thy desires; therefore treasure up these words in thy heart. Be faithful and diligent in keeping the commandments of God, and I will encircle thee in the arms of my love.
21 Behold, I am Jesus Christ, the Son of God. I am the same that came unto mine own, and mine own received me not. I am the light which shineth in darkness, and the darkness comprehendeth it not.
22 Verily, verily, I say unto you, if you desire a further witness, cast your mind upon the night that you cried unto me in your heart, that you might know concerning the truth of these things.
23 Did I not speak peace to your mind concerning the matter? What greater witness can you have than from God?
24 And now, behold, you have received a witness; for if I have told you things which no man knoweth have you not received a witness?
It is important that it be remembered that this revelation was given by the Spirit to the Prophet Joseph Smith who is dictating it to Oliver who is writing down the words. Therefore, when it comes through Joseph Smith revealing the time that Oliver had peace spoken to him (that only he and the Lord knew about) he then realizes that Joseph Smith is a conduit of the Spirit which is a sign to Oliver that the work is true. It is important to note that the Lord uses the word "instruction" in verse 14. He doesn't give yes and no answers but instead he give experiences which instruct and which allows the receiver to come to correct conclusions.
Then again Oliver is given another revelation where the Lord explains the revelatory process:
2 Yea, behold, I will tell you in your mind and in your heart, by the Holy Ghost, which shall come upon you and which shall dwell in your heart.
3 Now, behold, this is the spirit of revelation; behold, this is the spirit by which Moses brought the children of Israel through the Red Sea on dry ground.
We are taught in the Law of Moses that in the mouth of two or more witnesses every truth will be established. Notice that the Lord has two places in our body that receives revelation - our heart and our mind. The two must be in agreement with each other to establish the truth of the revelation. Sometimes the feeling in the heart is also called a burning of the bosom:
7 Behold, you have not understood; you have supposed that I would give it unto you, when you took no thought save it was to ask me.
8 But, behold, I say unto you, that you must study it out in your mind; then you must ask me if it be right, and if it is right I will cause that your bosom shall burn within you; therefore, you shall feel that it is right.
9 But if it be not right you shall have no such feelings, but you shall have a stupor of thought that shall cause you to forget the thing which is wrong; therefore, you cannot write that which is sacred save it be given you from me.
Notice that much of revelation deals with "feelings." That is very important. One must learn to know when the spirit is present and when it is confirming an answer by the feelings one receives.
As in the D&C 6:14-24 revelation - speaking peace to ones mind is a feeling.