This is the 3rd and final temptation in Matthew, chapter 4:8-10, but here in Luke it is the 2nd temptation. The wording is almost the same, indicating a shared common source, perhaps Q. Luke said that the devil led Jesus up (Καὶ ἀναγαγὼν αὐτὸν), presumably a high mountain, as in some Orthodox manuscripts and in Matthew. He then showed him (ἔδειξεν αὐτῷ) in an instant or moment in time (ἐν στιγμῇ χρόνου), all the kingdoms of the world (πάσας τὰς βασιλείας τῆς οἰκουμένης). Exactly how he did this is difficult to discern. This time, the devil took Jesus to an exceeding high mountain, where he showed Jesus all the great kingdoms of the world. Luke was more restrained in his description of the various kingdoms, since he did not mention their splendor and glory, the way that Matthew had.
This is similar to Matthew, chapter 26:70-71, and Luke, chapter 22:57-58. John, chapter 18:17, has a simple denial. Peter was warming himself at the fire in the high priest’s courtyard, when a young servant girl of the high priest came up to him and said that he had been with Jesus. Mark said that Peter denied this (ὁ δὲ ἠρνήσατο). Peter said that he did not know or even understand what she was talking about (λέγων Οὔτε οἶδα οὔτε ἐπίσταμαι σὺ τί λέγεις). Then Peter walked away into the forecourt, the porch, or gateway to the courtyard (καὶ ἐξῆλθεν ἔξω εἰς τὸ προαύλιον). Some ancient Orthodox manuscripts had the cock crow at this point (καὶ ἀλέκτωρ ἐφώνησεν). This first denial story of Peter, the great leader and follower of Jesus, was in all 4 gospels. Not all leaders are perfect.
This is a unique saying of Mark. He indicated that Jesus said that everyone would be salted with fire (Πᾶς γὰρ πυρὶ ἁλισθήσεται). This eternal fire would be seasoned with salt to give a further sting. Some ancient orthodox manuscripts added here that every sacrifice would be salted with salt. (καὶ πᾶσα θυσία ἁλὶ ἁλισθήσεται). In other words, this spice or preservative salt would further enhance and lengthen the eternal fire of Gehenna or hell.
This verse is found only in some orthodox manuscripts because it is an exact repeat of what was said earlier in chapter 4:9 and 4:23. However, this warning was in all 3 synoptic gospels, in Matthew, chapter 13:8, and in Luke, chapter 8:8, and here. Jesus warned that anyone with ears to hear should listen (εἴ τις ὦτα ἀκούειν ἀκουέτω). Jesus often mentioned the importance of hearing and listening, something all of us should take heed.