The most accurate response to the question "How is this possible?" regarding the statement that "Earth is closest to the sun in January when it is winter in the Northern Hemisphere" is:
The angle at which the sun strikes Earth is more important than the distance.
This is because the seasons are primarily caused by the tilt of the Earth's axis, rather than its distance from the sun. During winter in the Northern Hemisphere, the tilt causes the sun's rays to strike at a more oblique angle, resulting in less direct sunlight and cooler temperatures, despite the Earth being at its closest point (perihelion) to the sun.