turn somebody/something down: means "to reject or refuse to consider an offer, a proposal, etc. or the person who makes it"
What is the opposite of "She turned him down" or "she turned his proposal down" in spoken language?
we can list formal words such as "accept", "consent", "agree" etc, which are common in written language.
"turn down" is used more in spoken language and its opposite should be more common in spoken language.