'two-part' is formed in Modern English by combining the numeral 'two' (from Old English 'twa') with the noun 'part' (from Old French 'part', Latin 'pars'), meaning 'a portion or division.'

'part' entered English via Old French 'part' (from Latin 'pars'); the pattern of combining a numeral with 'part' (e.g., 'two-part') is a straightforward compound formation in Modern English and developed by analogy with other numeral + noun compounds.

Originally the elements meant 'two' and 'a portion/division'; the compound has retained the literal meaning of 'made of two parts' and has been used attributively (before nouns) and predicatively over time.