C. He is cautious and thoughtful, preferring to plan ahead.
The evidence: The stage direction “(Pausing thoughtfully)” tells us how the line is to be spoken before he even opens his mouth. And what he says is a two-part thought — first the difficulty (“Gaining an audience with the King is no simple task”), then the response to it (“We need to devise a strategy”). Naming a problem and proposing a method is the mark of a planner.
The others fail on the same evidence: he doubts the task, not their abilities, and he does not suggest giving up (A); wanting a strategy is the opposite of rushing in (B); and he is the one making the suggestion, not waiting for someone else to (D).
Try This: Compare Har Datt here with Tenali Rama on page 3 — “this needs a well-planned approach, and I may need time to find the right strategy.” Two very different pieces, almost the same sentence. Both writers use it to mark the character who thinks before acting.