Concept:
The word puckish refers to a playful, mischievous, teasing, or humorous nature. A puckish person enjoys light-hearted jokes and playful tricks.
Step 1: Understand the meaning of the word.
In the sentence,
\[
\text{"The actor knew how to put off the media queries in a puckish manner."}
\]
the actor is handling questions in a playful and humorous way.
Step 2: Analyze the options.
• Mischievous -- similar in meaning to puckish.
• Grave -- serious and dignified.
• Grim -- gloomy or depressing.
• Solemn -- serious, formal, and not playful.
Step 3: Find the antonym.
Since puckish means playful and mischievous, its opposite is solemn, which means serious and formal.
\[
\boxed{\text{Solemn}}
\]