Step 1: Read the sentence.
The sentence is 'He approached her to marry him, but she ____ his proposal immediately.' We must choose the right phrasal verb.
Step 2: Understand the context.
A marriage proposal was made, and the word 'but' shows she did not accept it. So we need a phrasal verb that means 'rejected'.
Step 3: Recall the meanings.
'Turned away' means sent someone away. 'Turned down' means refused or rejected. 'Turned against' means became hostile. 'Turned back' means returned.
Step 4: Match the meaning needed.
We need the sense of refusing a proposal. 'Turned down' carries exactly that meaning, to reject an offer.
Step 5: Check it in the sentence.
'She turned down his proposal immediately' reads smoothly and means she refused it at once. So it fits.
Step 6: State the conclusion.
The correct phrasal verb is 'turned down'.
\[ \boxed{\text{turned down}} \]