Question

what was President Regan’s goal when he said: “General Secretary Gorbachev, if you seek peace, if you seek prosperity for the Soviet Union and Eastern Europe, if you seek liberalization: Come here to this gate. Mr. Gorbachev, open this gate. Mr. Gorbachev -- Mr. Gorbachev, tear down this wall!”

Answer 1

Reagan is trying to motivate the crowd to agree with him and support the argument of tearing down the Berlin wall. He is addressing Gorbachev by presenting options that are difficult for a politician to disagree with (who is going to outright say they don't want peace?), so that the audience will be able to accuse him of not wanting peace if he does not tear down the wall. 

Answer 2

President Ronald Regan’s goal for this speech was to see the destruction of the Berlin Wall.  However, it was not just the destruction of the wall that President Ronald Regan was calling for.  The call for the taking down of the wall was really a call to end the Communist rule over East Germany.  An end to Communist control over East Germany would have seen the beginning of peace and stability across Eastern Europe, which is what the goal really was by President Ronald Regan’s saying “Mr. Gobachev, tear down this wall!”