Step 1: Understanding the Question:
This question tests the correct selection of a preposition to form an adverbial phrase of manner.
The sentence describes the manner in which "he" accepted the criticism, using the noun "equanimity" (which means mental calmness and composure).
Step 2: Key Formulas and approach:
When describing the state of mind or manner in which an action is performed, we often use prepositional phrases.
We need to find the preposition that correctly links the action "accepted" with the state of composure "equanimity".
Step 3: Detailed Explanation:
$\bullet$ The phrase "with equanimity" is a well-established English idiom meaning to bear or accept something calmly and composedly.
$\bullet$ Prepositions like "into" suggest movement or transformation, which is inappropriate here.
$\bullet$ Prepositions like "for" represent purpose or duration, which does not fit the context.
$\bullet$ Preposition "in" is not used with equanimity to express the manner of acceptance.
Step 4: Final Answer:
Therefore, the correct preposition is "with", corresponding to Option (C).