Read the sentence. The peripheral nervous system—which is a network of nerves extending from your brain and spinal cord to all parts of your body carries signals back and forth. Which revision of the sentence is now properly punctuated? The peripheral nervous system—which is a network of nerves extending from your brain and spinal cord to all parts of your body carries signals back and forth. The peripheral nervous system (which is a network of nerves) extending from your brain and spinal cord to all parts of your body carries signals back and forth. The peripheral nervous system which is a network of nerves extending from your brain and spinal cord to all parts of your body carries signals back and forth. The peripheral nervous system—which is a network of nerves extending from your brain and spinal cord to all parts of your body—carries signals back and forth.

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pmayl
The correct form is the last one: 
The peripheral nervous system—which is a network of nerves extending from your brain and spinal cord to all parts of your body—carries signals back and forth.
The dashes help specify a separate clause, which explains what the peripheral nervous system is. 

The revision that shows the correct punctuation is D. The peripheral nervous system—which is a network of nerves extending from your brain and spinal cord.

What is punctuation?

Punctuation simply means the use of spacing, signs, etc to enable readers understand a passage.

In this case, the sentence that uses the correct punctuation is "The peripheral nervous system—which is a network of nerves extending from your brain and spinal cord to all parts of your body—carries signals back and forth".

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