IPA: /ˈkaʊntərˌɔːfər/
KK: /ˈkaʊntərˌɔfər/
A response to an initial offer, where the person making the counteroffer proposes different terms instead of accepting the original offer.
After reviewing the job offer, she decided to make a counteroffer with a higher salary.
Counteroffer → It is formed from "counter-" (meaning against or in response) and "offer" (from Old English "offrian", meaning to present or propose). The word "counteroffer" means a proposal made in response to a previous offer, essentially presenting an alternative.
Think of making a proposal "against" or in response to another offer — that's why a counteroffer is a new proposal in response to the first.
No commonly confused words.