Where did the devil take Jesus first, the pinnacle or somewhere else?

Matthew 4:5, 8 and Luke 4:5, 91

(Luke 4:5) - "And he led Him up and showed Him all the kingdoms of the world in a moment of time."
(Matt. 4:5) - "Then the devil took Him into the holy city and had Him stand on the pinnacle of the temple,"
(Luke 4:9) - "And he led Him to Jerusalem and had Him stand on the pinnacle of the temple..."
(Matt. 4:8) - "Again, the devil took Him to a very high mountain and showed Him all the kingdoms of the world and their glory."

There is no contradiction or difficulty here. All we need to do is put the verses from each gospel side by side to see the order of events. When we do that, we see that Jesus was led to high places three times. Take a look at the chart below.

We quickly see that Luke 4:5 is the first mention of Jesus being taken anywhere and it simply says, "And he [the devil] led Him [Jesus] up and showed Him all the kingdoms of the world in a moment of time." It isn't until later in Luke 4:9 that Jesus is lead to the pinnacle on top of the temple. Therefore, the answer is simple: Jesus was "led up" and was shown the kingdoms of the world. Later He was led to the pinnacle.

To see the entire context of each of the verses, in order and compared to each other, please see the grid below.

Event	Matthew 4:1-11	Luke 4:1-13
Jesus in wilderness	1 Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil.	1 Jesus, full of the Holy Spirit, returned from the Jordan and was led around by the Spirit in the wilderness
40 day fast	2 And after He had fasted forty days and forty nights, He then became hungry.	2 for forty days, being tempted by the devil. And He ate nothing during those days, and when they had ended, He became hungry.
turn stones to bread	3 And the tempter came and said to Him, "If You are the Son of God, command that these stones become bread."	3 And the devil said to Him, "If You are the Son of God, tell this stone to become bread."
"not by bread alone"	4 But He answered and said, "It is written, 'MAN SHALL NOT LIVE ON BREAD ALONE, BUT ON EVERY WORD THAT PROCEEDS OUT OF THE MOUTH OF GOD.'"	4 And Jesus answered him, "It is written, 'MAN SHALL NOT LIVE ON BREAD ALONE.'"
devil showed Jesus the kingdoms		5 And he led Him up and showed Him all the kingdoms of the world in a moment of time.
devil to give domain to Jesus		6 And the devil said to Him, "I will give You all this domain and its glory; for it has been handed over to me, and I give it to whomever I wish.
false worship		7 "Therefore if You worship before me, it shall all be Yours."
true worship		8 Jesus answered him, "It is written, 'YOU SHALL WORSHIP THE LORD YOUR GOD AND SERVE HIM ONLY.' "
devil took Jesus to pinnacle of temple throw yourself down	5 Then the devil took Him into the holy city and had Him stand on the pinnacle of the temple, 6 and said to Him, "If You are the Son of God, throw Yourself down; for it is written, 'HE WILL COMMAND HIS ANGELS CONCERNING YOU'; and 'ON their HANDS THEY WILL BEAR YOU UP, SO THAT YOU WILL NOT STRIKE YOUR FOOT AGAINST A STONE.'"	9 And he led Him to Jerusalem and had Him stand on the pinnacle of the temple, and said to Him, "If You are the Son of God, throw Yourself down from here; 10 for it is written, 'HE WILL COMMAND HIS ANGELS CONCERNING YOU TO GUARD YOU,' 11 and, 'ON their HANDS THEY WILL BEAR YOU SO THAT YOU WILL NOT STRIKE YOUR FOOT AGAINST A STONE."
don't test God	7 Jesus said to him, "On the other hand, it is written, 'YOU SHALL NOT PUT THE LORD YOUR GOD TO THE TEST.' "	12 And Jesus answered and said to him, "It is said, 'YOU SHALL NOT PUT THE LORD YOUR GOD TO THE TEST.' "
took Jesus to high mountain	8 Again, the devil took Him to a very high mountain and showed Him all the kingdoms of the world and their glory;
devil to give domain	9 and he said to Him, "All these things I will give You, if You fall down and worship me."
worship and serve God only	10 Then Jesus said to him, "Go, Satan ! For it is written, 'YOU SHALL WORSHIP THE LORD YOUR GOD, AND SERVE HIM ONLY.' "
	11 Then the devil left Him; and behold, angels came and began to minister to Him.	13 When the devil had finished every temptation, he left Him until an opportune time.