According to eyesenck's theory, activation in what brain area is thought to be involved in the dimension of introversion-extroversion?

Answer is Ascending reticular activating system found in the brain stem part of the brain.

Explanation:

Extroversion is the ability of being out-spoken and mixing with people freely and easily, thriving to be around people. And people with these abilities are regarded as extroverts. Introversion is the opposite of extroversion, where people prefer to be alone, not mixing with people freely or easily. People with such characteristics are called introverts.

The Eyesenck's theory explained introversion-extroversion as the rate, degree or extent an individual interact with other people. He specifically associated this to the physiology of the brain, and arrived at the activation of a pathway in the brainstem, which is known as the ascending reticular activating system.

Note that the brain stem comprises of the midbrain, medulla oblongata, Pons and the hindbrain.