The matthew Gospel details how wise men followed a start to palestine and asked Herod for permission to pay honor the newborn king (Jesus). According to the Encyclopaedia Britannica, herod was murdered in 4 BC. Matthew Gospels, therefore, places the birth of Jesus prior to 4 BC
On the Other Hand, The Luke Gospel places birth of Jesus after Cryrenius became governor of Syria in AD 6, ten years after the death of Herod. The author of the Luke Gospel beings by stating that various different accounts of the Gospel story haven been circulating and he was endeavoring to set the story straight once and for all. For this reason, he mentioned that the birth of Jesus took place during a census ordered by Caesur Augustus. It is important to note that this census took place while Cyrenius was governor of Syria. The author of the Luke Gospel mentioned this census to fix a point in time in which these events took place, namely while Augustus was Caesar (from years 27 BC to AD 14) and while Cyrenius was governor of Syria (AD 6 to AD 39). This means that Jesus Birth would have taken place between AD 6 and AD 14- Long after Herods Death. Therefore according to the Luke Gospel, the MAtthew Gospel cannot be true. The other point of view is that the Matthew Gospel is true and Jesus was Born before 4BC (Herods Death). This would mean that the Luke Gospel, insofar as the account of Jesus birth at the time of the census of Caesar Augustus, is not ture.
Clearly, either the Matthew Gospel is partly Fiction or the Luke Gospel is partly fiction. However they cannot be both true. Furthermore, if any part of the book is not true, how can this same book be the one and only word of God?