If someone is perplexed, it just means that they're confused or baffled. In the excerpt "Arriving at Emerald City," it's the little green man who shakes his head in perplexity.

As the title of the excerpt would suggest, Dorothy and her companions have just arrived in the Emerald City. When the little green man asks Dorothy and her companions what they wish in the Emerald City, Dorothy tells him that they came to see the Great Oz, the wonderful wizard himself.

It's then that the little green man shakes his head in perplexity, or puzzlement. He's so surprised at Dorothy's request that he has to sit down and think things over. It's been many years since anyone asked to see the Wizard. What makes the little green man so perplexed is that he doesn't understand why anyone would want to do this.

As he explains, the Wizard is powerful and terrible. If anyone should approach him on a foolish errand then they're liable to be destroyed. To be sure, the Wizard's no tyrant; as the little green man says, he's a good man who rules the Emerald City wisely and well. But he has no time whatsoever for those who aren't honest or approach him in a spirit of curiosity.