These adjectives have opposite meanings.
Prone means “lying face-down”—lying with the front of the body facing the floor.
Supine means “lying or sitting face-up,”—lying flat on the back, or leaning back in a comfortable chair.
Both words also have common metaphorical meanings . . .
Prone can mean “tending or likely” to do something, such as a habit. It is used in two patterns:
Julia was prone to correct people’s grammatical errors. (prone to + verb)
Ron was accident-prone. (noun + prone)
In these uses, you may think of prone as “leaning forward, towards” an action.
Supine can also mean idle, passive, or apathetic (not-caring). Think of a person lying back in a chair instead of doing their work; supine can have the negative connotations of lazy and irresponsible.