Ayin Tachat Ayin = ‘an eye instead of/underneath an eye’
Q: How do we know that it’s talking about monetary damages?
Answer: That’s in the mesorah. It was told to Moshe at Har Sinai, as part of the Oral Torah.
But, there are also a few hints in the wording:
For exammple, the Vilna Gaon points out: Tachat=underneath – the letters underneath the word Ayin is peh, kaf, samech, spelling kesef=money