constructive inference: when crest from one source meets a crest from another source, energy combine to displace the medium. Something occurs when trough meets through.
destructive inference: when a crest and trough meet, the energies combine to work against each other. they tend to cancel each other.
standing waves: when interfering waves have the same amplitude and wavelength, so the resultant interference pattern remains nearly stationary.
The answer to the question: Destructive inference because those headphones produce the necessary sound waves and add them to the headphone, therefore, they cancel the disturbing sound.