How free will and determinism are compatible?

They are compatible in the sense that we have to act responsibly regardless of any logical contradiction in these concepts, and without knowing the truth for ourselves, they are just concepts.

Determinism says if it rains, you gotta deal with it. That is why they say we have 'will', but not 'free will'.

http://www.naturalism.org/freewill.htm Look at the variety of authors, and the subjects that go with this debate. Anyone who says determinism has your life all laid out for you is talking about fate.

Compatibilism is the theory that we can be both caused and free. It is advocated by many modern philosophers, including the prolific and influential Daniel Dennett. http://www.philosophynow.org/issue62/Compatibilism

But the best explanation of the free will problem in the face of things we cannot control is this:

"...that which you call “free will” is your mind’s freedom to think or not, the only will you have, your only freedom, the choice that controls all the choices you make and determines your life and your character." Ayn Rand

There are certain things that should not be explored too deeply.

What keeps us all sane and accountable is the subjective feeling of having free will; whether there is truly free choice is something we will pretend to ignore.

That's one way to see it.

Here's another:

You are free to choose what you want.

What you want is determined (by you and your nature).

So in that view, you are free to choose what you already determined you want.