In following etymological information, what is the meaning of the word autogenous?
index: latin indicis "pointer, sign, list"
ambidexterity: greek ambi "both" + dex "right-handed"
degenerate: latin de "off, away from" + generare "to beget, produce"
autonomy: greek autos "self" + nomos "custom, law"
autopsy: greek autos "self" + opsis "a sight"
sign of increased production
self-replicating bacteria
self produced
a self-governing state

So let's look at the word 'autogenous' - it seems to have two stems - the stem 'auto' and the stem 'geno'. When we look at the list of terms your teacher has provided, the stem 'auto' means 'self' and 'geno' means 'to beget, produce'. The term 'beget" is a fancy word that means to cause something to happen or exist; to give rise to. 

Taking all of that info I would combine it to get 'self producer' and therefore choice is C. Hope that explanation makes sense. 

The answer is self produced. Hope it helps.