I don't care if you didn't hear what I said. That is your problem: a total ____________ to listen to anything I say to you.

The correct answer is "inability," which denotes a lack of ability to do something. In this context, the speaker is expressing frustration about the listener’s failure to engage or listen. The term conveys a complete absence of the capability to listen, effectively highlighting the listener's problem in a clear and straightforward manner.

The word "ability" suggests having the power, skill, or means to do something but does not imply the issue of not being able to listen in this context. "Capable" is an adjective that describes someone who possesses the required skills or qualities but does not fit grammatically in the sentence, as it does not convey the idea of failure or lack in the same way. Lastly, "possibility" refers to the chance or likelihood of something happening, which does not align with the intended meaning of the inability to listen. Hence, "inability" is the most appropriate choice, as it accurately reflects the sense of not being able to listen.