“Free will” is when we decide for ourselves what we will do, free of coercion or other undue influence.
“Determinism” asserts that the behavior of objects and forces in our universe provides perfectly reliable cause and effect, and thus, at least in theory, is perfectly predictable.
Because reliable cause and effect is neither coercive nor undue, it poses no threat to free will. A man holding a gun to our head forcing us to do his will is a meaningful constraint upon our choices. But reliable causation is not.
Because our decisions are reliably caused by our own thoughts and feelings, our deliberate choosing poses no threat to determinism. Our purpose and our reasoning are the causes of our deliberate choices.
Each choice we make for ourselves is both freely chosen and reliably caused. Thus, the concepts of free will and determinism are naturally compatible.
The illusion of conflict is created by a logic error called the “reification fallacy“. This happens when we mistakenly treat the concept of “reliable cause and effect” as if it were an external force controlling our choices, as if it were not actually us, simply being us and doing what we do.
But concepts are not “things” that cause. Only the actual objects themselves, and the forces they naturally exert upon other objects, can cause events to happen.
When empirically observed, we find that we exist in reality as physical objects, living organisms, and an intelligent species. As living organisms, we act purposefully to survive, thrive, and reproduce. As an intelligent species, we act deliberately by imagination, evaluation, and choosing. And, when we act upon our choices, we are forces of nature.
Reliable cause and effect is not an external force. It is us, and the rest of the physical universe, just doing what we do. Those who try to turn it into a boogeyman robbing us of our choices are empirically mistaken.
For a more formal treatment, see my analysis of the SEP article on “Causal Determinism”, in Determinism: What’s Wrong, and How to Fix it