Not years before, but afterwards. Essentially, the question is about the census mentioned in Luke's Gospel, where he talks about a census in the time of Quirinius as governor of Syria. The problem is that Josephus doesn't mention a census under Quirinius until 6AD, and we don't have any evidence that Qurinius was governor earlier.

The possibilities are:

1. Luke was mistaken (i.e. wrong but didn't know it)
2. Luke was lying (i.e. wrong and knew it)
3. Luke was accurate but we don't have enough data to verify it
4. We have misunderstood what the text is saying.

I write about it in slightly more depth in this comment thread here and here.