Matthew, Mark and Luke are called the synoptic Gospels because you can set them side by side and see the same events through the same general lens. John stands apart.
Put the three in parallel and two things jump out. The overlap is enormous, sometimes down to identical wording. And the differences are constant, in detail, order and emphasis.
That combination is what people mean by the synoptic problem. It is not a scandal and it is not hidden. It is just a question: how did three accounts come to be this similar and this different at the same time?
See it before you theorise about it
Do not take my summary. Open the synoptic parallels and look at an actual passage in all three columns.
You will see it immediately. Long stretches where the Greek runs nearly word for word. Then a detail present in one and absent in another. A different order of events. One Evangelist telling you there were two men and another mentioning one.
Look at it yourself for ten minutes before you read anyone's explanation, including mine. You will form better questions.
What the differences are and are not
The differences are almost entirely of this kind: detail, order, emphasis, and how much of a scene is told.
They are not of this kind: Jesus is God in one and not in another. He rises in one and stays dead in another. He teaches forgiveness in one and revenge in another.
That distinction is the whole thing, and it gets deliberately blurred by people arguing in bad faith. Two witnesses to a car accident who disagree about whether the light was amber or red are not giving contradictory accounts of whether there was a crash.
Ancient writing also did not work like a court transcript. Compressing a scene, arranging material by theme rather than by clock, reporting the substance of what someone said rather than a recording of it, these were normal and honest practices. Judging them by the standards of a modern deposition is an anachronism, not a discovery.
Why the similarity is the interesting half
Everyone fixates on the differences. The similarity is far more striking.
Three documents, written by different men, sharing long passages in nearly identical Greek. That does not happen by coincidence. It means there was a common source: shared written material, shared oral preaching, or dependence between them.
Which is exactly what the Church has always claimed. The Gospels come out of the apostolic preaching. There was a body of teaching being handed on, in fixed forms, before anyone wrote a Gospel. St. Luke says so at the start of his own book, that many had undertaken to compile accounts, and that these came from those who from the beginning were eyewitnesses.
He tells you his method in the first four verses. Read them. He is not claiming a vision. He is claiming research.
Where I would be careful
Two cautions, one in each direction.
Do not stake your faith on a particular scholarly solution about which Gospel used which. Those theories are reasonable and they are also revisable, and the Church has never dogmatised one. If your apologetic depends on a source theory, it is borrowed and it will let you down.
And do not respond to the whole question by pretending the differences are not there. They are there. Anyone can open the parallels and see them in thirty seconds. A faith that requires you not to look at the text is not worth having, and it will collapse the first time somebody makes you look.
Always have critical thinking. If you suspend it, you are in a cult. Follow the reason all the way through and it does not end where the sceptics say it ends.
What the Fathers do
St. Augustine wrote an entire work on this called The Harmony of the Gospels, and it is in the Fathers Library in full. A Father of the Church sat down and worked through the parallel accounts systematically, in the fourth century, precisely because he knew people noticed.
Read it and you will see the posture I want you to have. Not panic. Not denial. Careful attention to what each Evangelist is doing and why.
- Open the synoptic parallels and work through one event in all three.
- Read the surrounding chapter in each Gospel in the reader, because context usually explains the emphasis.
- Read Augustine's Harmony and Chrysostom's Homilies on the Gospel of Matthew in the Fathers Library.
Four men, four angles, one Christ. If they matched perfectly you would be told they colluded.