Of necessary consideration, but not always easy to deal with, in terms of understanding the Gospels, is an ancient literary ideal of arrangement that easily explains why the Gospels might give information in what appears to our eyes to be differing chronological order. In actuality the material may or may not be in chronological order -- and we should not make assumptions that it is unless clear chronological or other markers are present.
As we have pointed out elsewhere, the Gospels are ancient biographies. Ancient biographies, because they were not strictly history, arranged material either chronologically or topically, depending on the author's purpose. Hence the scattering and re-organizing of the Gospel material is recognizable as a normal process. Matthew, Mark and Luke had the "right" within their genre to order material as they pleased.
The ancient rhetoritician Quintilian wrote:
It has sometimes proved the more effective course to trace a man's life and deeds in due chronological order, praising his natural gifts as a child, then his progress at school, and finally the whole course of his life, including words as well as deeds. At times on the other hand it is well to divide out praises, dealing separately with the various virtues, fortitude, justice, self-control and the rest of them and to assign to each virtue the deeds performed under its influence.
And Samuel Byrskog, in Story as History , notes a secular example:
As for speeches, we have the rare opportunity of comparing Tacitus' version of Claudius' oration in favour of the admission of Gallic nobles to the Senate with the rather extensive, though discontinuous, fragments of the same speech preserved on a bronze tablet at Lugdunum...While Tacitus strongly rearranges and condenses the speech in order to sharpen the arguments, it is evident that he had some kind of raw material at his disposal....Cicero himself describes Caesar's commentarii as material from which would-be writers of history could select. Although he subsequently makes clear that historians might prefer the brevity to the "curling irons", he implies that this kind of information could then be subject to rhetorical elaboration....
This principle can be easily seen to have an extension in Matthew in particular, who has clustered teachings of Jesus but not always chronologically, versus Luke, who has followed the chronological model more closely, and how both have on various occasions tailored a work for a particular audience to make the message intelligible. The bottom line is that difference in arrangement is not always difference in chronology and above all is not to be automatically construed as error.
Keener [Matthew commentary, 16ff] further notes that ancient writers of biographies gave themselves considerable latitude in composition which match those we find among the Gospels. A biographer could start in adulthood (as did Mark; hence, no argument is valid making light of a lack of mention of the virgin birth); they "also had the freedom to rearrange their material topically rather than in chronological sequence" and "could expand or abridge accounts freely". Ancient historians could also tell the same event differently, even the same author, in different works, to stress an angle they wished to emphasize.
A good example of this paradigm at work would be Luke's "version" of Jesus' first sermon in Luke 4:16-30. This is obviously not the same story as found in Mark and Matthew in their chronology, yet it is obviously intended to take the place of the same story. Luke places this story here for thematic, rather than chronological reasons; and the ancient reader would know this and would not raise a fuss when they saw Matthew and Mark report differently.
Luke even shows that he knows this was not Jesus' first public appearance (for he alludes to work done at Capernaum, which Luke does not report -- 4:23) but he has placed it in his Gospel as a sort of "keynote speech" laying out themes Luke will pursue. The speech here summarizes the nature of Jesus' synagogal preaching (mentioned elsewhere in Luke, but not reported elsewhere in detail). It also serves as an inclusio for the entire Luke-Acts complex, as Luke 4:16-30 shows rejection of the message of salvation by Jews and anticipates its acceptance by Gentiles, while Acts 28:17-28 the anticipation fulfilled.
In close: Consideration of the principles of ancient literary arrangement are an important factor in study and reconciliation of the Gospel accounts.