The phrase "hast right" is an archaic term that was once used to mean "you are correct." The spelling may seem unusual to modern ears, but it is consistent with the pronunciation of the time. In IPA phonetic transcription, "hast" would be written as /hæst/, with the "a" pronounced as a short vowel sound. "Right" would be written as /raɪt/, with the "i" pronounced as a long vowel sound. Together, the phrase would be pronounced as "hast rite."
There is no specific word "hast right" in the English language. "Hast" is an archaic form of the verb "have", specifically the second person singular form of "to have" in the present tense. "Right" is a term indicating correctness or agreement. Therefore, if we assume you meant to ask about the phrase "have right", then its etymology can be traced back to Old English.
The word "have" comes from the Old English verb "habban", which meant "to own" or "to possess". "Right" has its roots in the Old English word "riht", meaning "just" or "fair". Over time, the meaning of "right" expanded to include correctness or agreement with a rule or principle.
Together, the phrase "have right" implies possessing correctness or being entitled to something.