There is certainly a place for extensive, detailed answers to questions about profound, complex matters. But there is also a place for brief, simple answers to such questions. Here is an attempt to simply and succinctly answer the question of how predestination and free will go together.
This is a big question that there is disagreement over among Christians. But I would say that, in the New Testament, predestination is a corporate phenomenon about God’s blessing he will bring about for his people, the Church, those whom the Bible says are “in Christ.” But individuals come to be in Christ by freely (there’s the free will) believing in Jesus, which also brings them to be part of his people and to get the benefits he gives to his people.
Here is an analogy from the Life in the Spirit Study Bible, pp. 1854-1855: Concerning election and predestination, we might use the analogy of a great ship on its way to heaven. The ship (the church) is chosen by God to be his very own vessel. Christ is the Captain and Pilot of this ship. All who desire to be a part of this elect ship and its Captain can do so through a living faith in Christ, by which they come on board the ship. As long as they are on the ship, in company with the ship’s Captain, they are among the elect. If they choose to abandon the ship and Captain, they cease to be part of the elect. Election is always only in union with the Captain and his ship. Predestination tells us about the ship’s destination and what God has prepared for those remaining on it. God invites everyone to come aboard the elect ship through faith in Jesus Christ.