Four compounds are shown beside the options (the drawn compound is ethene, for reference). Which structure is the weakest acid?

Acidity follows the stability of the conjugate base. Ethyne (pKa about 25) is a far weaker acid than ethanol (about 16), phenol (about 10) and acetic acid (4.76); even though sp carbon is fairly electronegative, a carbanion with no delocalisation is much less stable than an oxyanion.