At Luke 4:44 this translation says that Jesus preached in the synagogues of Galilee. However, many other Bibles say that Jesus preached in the synagogues of Judea. Which is correct?
It depends on which Greek text you use as a reference. The Wescott/Hort text says he preached in Judea, while several other texts, including the Tischendorf Greek text, say that he preached in Galilee.
We have chosen to go with the Galilee, because the context makes it clear that he was preaching in Galilee at that time. The fact is, Jesus did little preaching in Judea until the last days of his life on earth, because the Judeans were always looking to kill him (see John 11:8).