The level of branching of common carotid artery:
COMMON CAROTID ARTERIES:
There are two common carotid arteries: right and left. They are the chief arteries of the head and neck.
Origin:
The right common carotid artery arises in neck from brachiocephalic trunk (innominate artery) behind the
sternoclavicular joint.
The left common carotid artery arises in thorax (superior mediastinum) directly from the arch of aorta. It ascends to the back of left sternoclavicular joint and enters the neck.
Course, Termination, and Relations:

In the neck, both arteries (right and left) have similar course.
Each artery runs upwards from sternoclavicular joint to the upper border of the lamina of thyroid cartilage (opposite the disc between the 3rd and 4th cervical vertebrae), where it terminates by dividing into internal and external carotid arteries.

Key Concept:
Left and right CCA runs upwards from sternoclavicular joint to the upper border of the lamina of thyroid cartilage (opposite the disc between the 3rd and 4th cervical vertebrae), where it terminates by dividing into internal and external carotid arteries.
Upper border of thyroid cartilage
Lower border of cricoid cartilage
Lower border of thyroid cartilage
Hyoid