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You’ll remember from earlier that palms up is a friendly gesture; palms down indicates a closed-off speaker who isn’t open to new ideas.
Someone who offers his hand to you with his palm facing down is telling you that he’s the top dog in the office. This is the kind of move that the president of the company might use when meeting with underlings. If someone offers you his hand in a palm-down position, it’s all right to offer yours vertically … and wait for him to shake your hand (unless he’s your boss). The funny thing is that some particularly aggressive people will take your hand and try to turn it palm up as they shake it. Go ahead and fight the twist, and don’t feel a bit strange about the wrist wrestling you’re engaging in. You’re simply protecting your own standing.