And when many days were fulfilled, the Jews took counsel together to kill him: (ASV)
"When many days had passed". Paul claims in Gal 1:16-18 that he did not consult anyone or go to Jerusalem until three years later, after going into Arabia and back to Damascus.
These events occur immediately after Paul has his Damascus Road experience and is blinded. Paul is brought to Damascus, regains his sight, and we then read:
19 So when he had received food, he was strengthened. Then Saul spent some days with the disciples at Damascus. 20 Immediately he preached the Christ in the synagogues, that He is the Son of God. 22 But Saul increased all the more in strength, and confounded the Jews who dwelt in Damascus, proving that this Jesus is the Christ. 23 Now after many days were past, the Jews plotted to kill him. 24 But their plot became known to Saul. And they watched the gates day and night, to kill him. 25 Then the disciples took him by night and let him down through the wall in a large basket. 26 And when Saul had come to Jerusalem,...
In Galatians 1, Paul provides this additional information.
15 But when it pleased God,... 16 to reveal His Son in me [on the road to Damascus]...I did not immediately confer with flesh and blood, 17 nor did I go up to Jerusalem to those who were apostles before me; but I went to Arabia, and returned again to Damascus. 18 Then after three years I went up to Jerusalem...
The Jews who plotted to kill Paul were located in Damascus. Paul preached in Damascus immediately after his sight returned. He went into the desert for a time and then returned to Damascus and began preaching again. It is at this point that the Jews in Damascus plot to kill Paul. Because of this, Paul then goes to Jerusalem. There is no conflict in the account.
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