The human body has four jugular veins

[Freeguy]

The human body has four jugular veins, ..... each side of the neck.

1. there are two on
2. it has two on
3. two are on
4. two on

Why WE should leave out ARE here? ( The correct answer is number 4.)

 

[Raymott]

The human body has four jugular veins, ..... each side of the neck.

1. there are two on
2. it has two on
3. two are on
4. two on

Why WE should leave out ARE here? ( The correct answer is number 4.)

Yes, 4 is right. Why have you emphasised WE? 'Are' is not necessary. If you added 'are', you'd have to make two sentences.
"The human body has four jugular veins. There are two on each side of the neck."
The "it has" has not been repeated in, "The human body has four jugular veins, [It (The human body) has] two on each side of the neck."
The subject and verb are the same for the second phrase; they don't need repeating.