Meaning of idiom “by the skin of his teeth”?

The idiom “by the skin of his teeth” means to succeed or escape by a very narrow margin, barely making it. It implies a close call or a near miss.

• Narrowly is the correct option because it perfectly captures the essence of the idiom, signifying a small margin or a close shave.
• Vastly means to a great extent or degree, which is the opposite of the idiom's meaning.
• Openly means publicly or without concealment, which is unrelated to the concept of a narrow escape.

Therefore, the phrase emphasizes a minimal difference between success and failure.