We have free will, but then how does the incident with Pharaoh and his heart being “hardened” work?

When Moses is first called by God to return to Egypt to lead Israel out of their bondage and slavery, God tells him, “When you return to Egypt, see that you perform before Pharaoh all the wonders I have given you the power to do. But I will harden his heart so that he will not let the people go—God speaking, Exodus 4:21. Moses therefore is put on alert as to what Pharaoh’s response to him is going to be. However, as the text continues, the initial times a “hardened heart” is mentioned, Pharaoh is doing it himself, of his own volition—his own, personal reaction to the words he is hearing from Moses. The first time is in the palace of Pharaoh himself, when Moses makes his initial request to let Israel go into the wilderness to offer sacrifices to God. When Aaron’s rod becomes a snake at Moses’ command, Pharaoh’s court magicians accomplish the same thing—even though Aaron’s snake swallows up the snakes of the magicians. But the Bible says, Yet Pharaoh’s heart became hard and he would not listen to them, just as the Lord had said—Exodus 7:13. But what is interesting is what God says in response to Pharaoh’s attitude: Pharaoh’s heart is unyielding; he refuses to let the people go—God speaking, Exodus 7:14. God is noting an attitude that already exists in Pharaoh. The next time is following the first plague that Moses presented—the turning of water to blood. When Pharaoh’s court magicians accomplished some version of the same thing, the Bible says, But the Egyptian magicians did the same things by their secret arts, and Pharaoh’s heart became hard; he would not listen to Moses and Aaron, just as the Lord had said. Instead, he turned and went into his palace, and did not take even this to heart—Exodus 7:22-23. The next time is following the second plague of the overrunning of the land by frogs. When relief occurs from this situation, again the Bible says, But when Pharaoh saw that there was relief, he hardened his heart and would not listen to Moses and Aaron, just as the Lord had said—Exodus 8:15. And so it continued—Pharaoh was himself hardening his heart against Moses and Israel. God simply knew that this was going to occur. Finally, we read these words following the plague of boils on the skin of both men and animals as Pharaoh continues to defy Moses: But the Lord hardened Pharaoh’s heart and he would not listen to Moses and Aaron, just as the Lord had said to Moses—Exodus 9:12. It appears that this is God’s judgment on Pharaoh as a result of his own refusal to bow to God’s sovereignty. In other words, Pharaoh had already demonstrated a refusal to bow to God’s will, so God now simply used his attitude of heart as a means of demonstrating His own power and authority. What this episode shows is two things: (1) God, both then and now, is ultimately in control, and the attitudes and actions of men make no impact on Him or His plans, and (2) God’s control of these or any other affairs—or His foreknowledge of these or any other events—does not resolve men of blame; like any other sinners, Pharaoh remained fully responsible for his refusal to obey God. God’s foreknowledge of Pharaoh also knew the final outcome of his life so, even in his disobedience, he became an instrument of God’s plan. This is not a matter of executing judgment against people who otherwise wanted to serve the Lord and His purposes, but rather against confirmed rebels. In Pharaoh’s case, it was a deserved judgment against someone who would never listen to and obey God.