Where does this quote come from? It does NOT look like a reliable source of information to me.
The dynamic range of the 16-bit quantizer is 6B = 6·16 = 96 dB.
Wrong. The quantization noise for a 16 bit bipolar rounding quantizer is about -101dB dFS. That makes the signal to noise ratio for a sine wave 98dB and for the "average" music file about 8dB-90dB.
Note that the dynamic range of the human ear is about 100 dB.
Grossly oversimplified and misleading. The dynamic range of human auditory systems depends highly on frequency (and unfortunately also and age and how much rock& roll you have played, sigh). Max dynamic range is about 120 dB at the midrange.
This is the reason why “CD quality” digital audio requires at least 16-bit quantization.
16-bit quantization was chosen as a complicated trade off between audibility of quantization noise and cost & technical complexity at the time the standard was created. 16-bit per se is in many cases not sufficient unless proper "dithering" and "noise shaping" is applied as well.
The explanation really misses the main point. SNR and audibility of quantization noise depends A LOT on frequency and the specific signal. 16-bit PCM quantization is a "brute force" approach with most bits being wasted and a few important ones missing. Perceptual codecs such as AAC, MP3, Ogg, etc. do this much better and generate way more "sound quality per bit".
Finally, the question:
How can we obtain(calculate) the fact that the dynamic range of the human ear is about 100 dB?
Through listening test performed over a wide range of diverse subjects and test signals. The hearing threshold is determined as the sound pressure where the subject says "I can't hear this anymore" and the pain threshold corresponds to "ow, that hurts. Stop it!". The pain threshold is particularly difficult to test since it's fairly subjective and the testing can cause physical damage to the test subject. The results of the hearing test are then compiled using statistical analysis. You end up with a set of curves like this: https://en.wikipedia.org/wiki/Equal-loudness_contour .