The centriole undergoes duplication during :

The correct answer is S-phase.

Explanation:
During the cell cycle, a eukaryotic cell goes through a series of phases to grow and divide. The interphase of the cell cycle is divided into three main stages: the G₁ phase (First Gap), the S-phase (Synthesis), and the G₂ phase (Second Gap).

The S-phase (Synthesis phase) is specifically characterized by the duplication of genetic material (DNA replication) in the nucleus.
Simultaneously, in the cytoplasm of animal cells, the centriole undergoes duplication. Centrioles are barrel-shaped organelles that play a crucial role in organizing the spindle fibers during cell division (mitosis).

Therefore, centriole duplication begins during the S-phase of interphase, ensuring that when the cell enters mitosis (specifically prophase), it contains two pairs of centrioles to migrate to opposite poles and form the mitotic spindle.