Alma 10:6 - 10:10
Alma 10:6 Nevertheless, I did harden my heart, for I was called many times and I would not hear; therefore I knew concerning these things, yet I would not know; therefore I went on rebelling against God, in the wickedness of my heart, even until the fourth day of this seventh month, which is in the tenth year of the reign of the judges.
Amulek confesses that he had rejected the Spirit of God that was trying to influence his life. Deep down in his soul, he knew that he was turning his back on it, but his selfishness was influencing him far more. This was the case up until the 4th day of the 7th month in the year 10 of the reign of the judges.
Alma 10:7 As I was journeying to see a very near kindred, behold an angel of the Lord appeared unto me and said: Amulek, return to thine own house, for thou shalt feed a prophet of the Lord; yea, a holy man, who is a chosen man of God; for he has fasted many days because of the sins of this people, and he is an hungered, and thou shalt receive him into thy house and feed him, and he shall bless thee and thy house; and the blessing of the Lord shall rest upon thee and thy house.
On the particular day while on a trip to see a family member, an angel appeared to Amulek. The angel told him to return to his house and be prepared to feel a prophet of the Lord. The reason being, that he had been fasting for many days to know what to do to get the people of Ammonihah to listen to him for he feared deeply for their lives and eternal welfare. And by taking this prophet in and caring for him, Amulek and household would be greatly blessed.
I'm guessing, but feel pretty certain, that the angel was the same angel that had appeared to him and commanded him to return to Ammonihah
Alma 10:8 And it came to pass that I obeyed the voice of the angel, and returned towards my house. And as I was going thither I found the man whom the angel said unto me: Thou shalt receive into thy house—and behold it was this same man who has been speaking unto you concerning the things of God.
Well, Amulek did return back to the city and sure enough, he meets the man he was told to help. And the man Amulek met was Alma who had just been speaking to the crowd.
Alma 10:9 And the angel said unto me he is a holy man; wherefore I know he is a holy man because it was said by an angel of God.
Amulek again reiterates, that the angel told him that Alma was a holy man and he gives his personal testimony to that fact.
Alma 10:10 And again, I know that the things whereof he hath testified are true; for behold I say unto you, that as the Lord liveth, even so has he sent his angel to make these things manifest unto me; and this he has done while this Alma hath dwelt at my house.
Amulek further testifies that the things Alma has testified to the crowd are true. Again the angel testified to Amulek that Alma was a holy prophet and all this was made know to Amulek while Alma was in his house.