'non-anthracenic' is formed from the negative prefix 'non-' (from Latin 'non', meaning 'not') and 'anthracenic' (from 'anthracene' + adjectival suffix '-ic'); 'anthracene' itself ultimately traces to Greek 'ἄνθραξ' ('anthrax'), meaning 'coal'.

'non-' + 'anthracenic' is a modern English formation; 'anthracenic' derives from 'anthracene' (a 19th-century name for a coal-tar hydrocarbon), and 'anthracene' was coined from Greek 'anthrax' ('coal') when the compound was isolated from coal tar.

The prefix 'non-' has consistently meant 'not'; combined with 'anthracenic' it has the straightforward modern meaning 'not anthracenic' (i.e., lacking anthracene-like structure), a technical descriptive coined for chemical classification.