Now the eleven disciples went to Galilee, to the mountain to which Jesus had directed them.
Matthew 28:16
And they rose that same hour and returned to Jerusalem. And they found the eleven and those who were with them gathered together,
Luke 24:33
As they were talking about these things, Jesus himself stood among them, and said to them, "Peace to you!"
Luke 24:36
The Claim: In Matthew 28:16, the risen Jesus first appeared to the group of eleven disciples in Galilee, but in Luke 24:33, the risen Jesus first appeared to the group of eleven disciples in Jerusalem. Both events couldn't have been the first to happen, so which happened first? How could the disciples be in both Galilee and Jerusalem at the same time?
The Explanation: Neither Matthew 28:16 nor Luke 24:33 make reference to which event happened first. The Bible verses give no priority to the order these events happened. In fact, if you read the entire chapters of Matthew 28 and Luke 24, there is no claim within the Bible verses about one event happening before the other. Therefore, the question of which event happened first does not even need to be addressed.
So now for the second question. How could the disciples be in both Galilee and Jerusalem at the same time? Again, these Bible passages do not claim that both events were happening simultaneously. In fact, the evidence is that these were 2 separate events happening at 2 different points in time.
If you continue to read through to the end of Matthew 28, you'll see that in verse 19 Jesus says "Go therefore and make disciples of all nations..." This phrase is not mentioned at all if you read through Luke 24:36-53, to the end of the chapter. In Luke 24:36-53, Jesus talks about prophecies being fulfilled, and the Law of Moses, and these things are not found in Matthew 28.
Therefore, it is logical to conclude that these are two separate events happening at two different times. This is not a contradiction.
Extra: There is the hint of a lingering question after the explanation. Why are the four Gospel accounts different? Why do they record different events? Why do some of the Gospels discuss certain events, while the event is omitted in another Gospel?
John gives us a very practical answer to these questions.
Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written.
John 21:25
The ministry of Jesus lasted about 3 years. It would not be practical to expect every single event and detail that happened in those 3 years to appear in the Bible. Each of the four Gospels record some of the things the disciples experienced, and the disciples recorded what they felt were the most important things to include. Of course, opinions differ on what all is important, and that's why there are events included in some Gospel accounts and omitted in others.