Final answer:
The question pertains to the technique used by Exekias, an ancient Greek vase painter, and the correct answer is Black-figure, which is indicated by his use of a black slip on red clay to create intricate designs.
Step-by-step explanation:
The work in question by Exekias is a celebrated example of black-figure pottery, a technique used for decorating ancient Greek vases, particularly during the Archaic period. This technique involves painting figures in a black slip on red clay pots and then firing them in a kiln in a way that the parts painted with slip turn black while the background of the pot remains red. As described in the student's question and supported by the reference to Exekias's work, the correct answer to the categorization of Exekias's pottery technique is B) Black-figure.
Exekias is renowned for his detailed and intricate lines, as well as his ability to evoke emotion through his art. His works, such as the Dionysos in a Sailboat scene, reflect the mastery of this ancient technique that predates the red-figure style, which started gaining popularity after 530 BCE with the works of the Andokides Painter. The black-figure style is characterized by the incision of details into the black silhouette, which allows for the underlying red color of the clay to show through and gives depth and detail to the depiction.