Final answer:
The proper technique for assessing the tympanic membranes of a 3-year-old child is pulling the auricle upward and backward. This technique helps straighten the ear canal for better visualization of the tympanic membrane.
Step-by-step explanation:
The proper technique for assessing the tympanic membranes of a 3-year-old child is pulling the auricle upward and backward (option b). This technique helps straighten the ear canal for better visualization of the tympanic membrane. Using an inverted otoscope grip (options a and d) or holding the handle of the otoscope between the thumb and index finger while the child lies on the weight scale (option c) are not recommended and may not provide a clear view of the tympanic membrane.