My question is about free will in Greek mythology. How do we explain that fate is also a thing while they also have free will?
The answer really depends on to which interpretation of free will you subscribe. I will greatly oversimplify the various philosophical interpretations of free will here into two camps:
Compatibilism is the belief that free will and determinism are mutually compatible and that it is possible to believe in both without being logically inconsistent. The oldest Greek school of philosophy that proposed this belief is stoicism
Incompatibilism is the view that a deterministic universe is completely at odds with the notion that persons have a free will; that there is a dichotomy between determinism and free will where philosophers must choose one or the other. In Ancient Greece, this would be more a religious view than a philosophy, i.e. our lives, to the tiniest detail, are written or spun by the fates
These two camps can be rendered into the following philosophical interpretations:
Hard determinism (determinism + incompatibilism)
Deterministic compatibilism (determinism + compatibilism)
Indeterminism/metaphysical libertarianism (indeterminism + incompatibilism)
Both Hard Determinism and Deterministic compatibilism existed in some form in Greek philosophy or religion. If for example we look at Oedipus, you can interpret the story with both of these perspectives. Indeterminism is more of a 20th-century philosophy.
Oedipus is a tragic hero, who accidentally fulfilled a prophecy that he would end up killing his father and marrying his mother, thereby bringing disaster to his city and family.
Deterministic compatibilism would read this story as: yes, free will and fate (Lat. fatum, "destiny", i.e. a form of "divine determinism") can co-exist. Oedipus has free will, but despite all willed actions to avoid his fate, the gods play a cruel trick on him and his free will, though existing, is overruled by divine determinism (fate) in the end.
The Hard Determinism interpretation would be: Oedipus only has the illusion of free will, circumstances (e.g. his environment & character) created by the gods (pre)determine the limited range of illusionary free will choices.