Two points here. First, 0 dB is the reference level of sound, in this case the threshold of hearing. This typically corresponds to a sound pressure of 0.00002 Pa, which is a very faint sound. Second, to read an audiogram, the y-axis is the softest sound heard at least 50% of the time.

So the data point at 3000 Hz of 40 dB is not a negative value. It means that a tone at 3000 Hz has to be at least 40 dB loud (about the level of a refrigerator humming) for him to hear it.

What you don’t see in a simple audiogram is that quality of life is not just about picking out tones. When the higher frequencies over the range used in speech drop out like this, it becomes harder to understand and pick out words in conversation.