Myth came into English in the early 19th century via Latin mȳthus “myth, fable” from Greek mŷthos. Latin mȳthus is straightforward: it means “a fable or myth,” such as one would read in Ovid’s Metamorphoses, and in Late Latin, mȳthus is even used as a synonym for fābula “a story, fable.”
Greek mŷthos has a tremendously wide range of meaning: “a word, a speech, mere speech (as opposed to érga ‘deeds’), something said, a thought, an unspoken word, a purpose, a rumor, a report, a saying, fiction (as opposed to lógos ‘historical truth’), the plot of a play, a narrative, a story, a story for children, a fable.”
Sixty percent of Greek vocabulary has no known etymology, and mŷthos is probably within that 60 percent, but it is possible that mŷthos comes from the uncommon Proto-Indo-European root mēudh-, mūdh- (with other variants) “to be concerned with, crave, earnestly desire, think over.” Following this theory, from the variant mūdh-, Greek derives mŷthos and its derivative verb mȳtheîsthai “to speak, converse, tell”; Gothic has maudjan “to remind, remember”; Lithuanian has maûsti “to be concerned with,” and Polish has myśleć “to think.”

Did you mean Hythe?