In the northern hemisphere, the longest day of the year normally occurs in the:

The correct option is Second half of the month of June.

To understand why this is correct, we can look at the astronomical cycle of the Earth's orbit and axial tilt.
The Earth rotates on an axis that is tilted by approximately 23.5 degrees relative to its orbital plane around the Sun. As the Earth orbits the Sun, this tilt remains pointed in the same direction in space. Consequently, the angle at which solar radiation hits different parts of the Earth changes throughout the year.

The longest day of the year in the Northern Hemisphere is known as the summer solstice. This is the moment when the North Pole is tilted most directly toward the Sun, causing the Sun to reach its highest path in the sky for Northern Hemisphere observers and resulting in the maximum duration of daylight.

This astronomical event typically occurs on June 20, June 21, or June 22 each year. Since the month of June has 30 days, the first half of the month corresponds to June 1 through June 15, and the second half corresponds to June 16 through June 30. Therefore, the summer solstice, occurring around June 21, falls securely in the second half of the month of June.