As I have said in an earlier post the internal evidence suggests that Jesus was born between 6 and 4BC during the closing years of the reign of Herod the Great and during a census ordered by Augustus. The problem with this dating is that, according to Josephus, Quirinius whom Luke places as Governer of Syria at the time of the census did not ascend to that rank until about 6AD, a 10 to 12 year difference.
There have been a variety of suggested solutions to the problem and the referenced article mentions two. The first being that the passage in Luke can be translated:
‘This census happened before Quirinius was in charge of Syria’
While this is possible answer the writer of the article points out that such a translation is inconsistant with normal Greek practise.
A second answer is to suggest that Quirinius was governor of Syria at an earlier stage but as the writer points out again; although there is evidence that someone was legate for a second time in Syria, that person is not identified and the gaps that could be filled by Quirinius are before 10BC and from 4-1BC. Neither of these frame the time period that Jesus' birth embraced.
The writer's conclusion is that Luke's information is faulty and perhaps it is; even a careful historian may preserve incorrect information. However let us see if there are other possible options available to us.
Could Josephus be at fault? The gospel of Luke is the precursor to the book of Acts which internal evidence suggests was composed about 60AD. It is therefore closer to the events than Josephus' own writings. As careful a historian as Luke was demonstrated to be by Sir William Ramsay should perhaps be given the benefit of the doubt. Nonetheless I do not favour this answer. Josephus too has been shown to be a careful historian.
Perhaps the simplest answer is to acknowledge that a combination of distance and the techniques available to the ancients did not fasciliatate rapid compilation and assessment of data. The census begun prior to the birth of Jesus was not completed until Quirinius took over the governership of Syria. This attempted harmonisation does seem to answer the point without requiring any of the recorders to be in error.
Ultimately we cannot know for sure what happened 2000 years ago. There are difficulties in understanding certain parts of the Bible. However claiming that we need 100% certainty in every aspect of the Bible erects a standard that few, if any, documents could meet. The basics of Christianity can be fairly well established by normal historical criteria. The evidence is sufficient; it is not exhaustive.