How to map modern meaning of Synecdoche, to its Greek morphemes ‘syn” + ‘ek” + ‘deskhesthai”?

According to Etymonline, Synecdoche means “figure of speech in which a part is taken for the whole or vice versa". Both English and Late Latin synecdoche hail from Greek synekdokhe "the putting of a whole for a part; an understanding one with another," literally "a receiving together or jointly." This is from synekdekhesthai "supply a thought or word; take with something else, join in receiving," from syn- "with" (see syn-) + ek "out" (see ex-) + dekhesthai "to receive," related to dokein "seem good" (from PIE root *dek- "to take, accept")”. How does the English meaning of Synecdoche correspond with these three Greek morphemes? To wit, how can we map these 3 Greek morphemes to the English meaning of Synecdoche? As I don't speak Greek, these Greek morphemes are literally Greek to me! I'm out of my depth relating these Greek morphemes to English. I shall appreciate someone connecting these dots for me! Thanks. First, the syn part is actually the precursor of sin-, the prefix for "with", and means the same, from PIE ksun, also "with". But how does the prefix Syn- relate to Synecdoche? “with” doesn’t show up in Etymonline's definition above - “figure of speech in which a part is taken for the whole or vice versa". What does “with” have to do with Synecdoche? The second component is that of ek, the precursor of ex-, the prefix for "out", and also means the same, from PIE eghs, also "out". How does Synecdoche involve outness, or outwardness? Finally, the root of the term is dokhe, which kind of meant "receive". This derives from the Proto-Indo-European term dek, which meant something more like "to accept". As a whole, when the parts are put together, a synecdoche really just means "without accepting". dekhesthai "to receive," related to dokein "seem good" (from PIE root *dek- "to take, accept"). What do Synecdoches receive? From whom or where or what do Synecdoches receive, whatever Synecdoches receive?