Final answer:
The art piece considered didactic or intended to teach is the Exodus and Crossing of the Red Sea from Dura Europos, which depicts a biblical story for educational purposes within a synagogue.
Step-by-step explanation:
The work of art that is considered didactic, or intended to teach, from the given options is likely the Exodus and Crossing of the Red Sea from Dura Europos. This piece, a wall painting from a third-century synagogue in Dura-Europos, modern-day Syria, depicts a biblical story and serves as an educational illustration of religious events for those who would view it within the context of the synagogue. The imagery directly conveys narratives from the scriptures, thus serving a didactic purpose.
Other pieces mentioned, such as the Reliquary of the Head of St. Alexander, and the mosaic of Emperor Justinian in San Vitale, Ravenna, serve more as testimonials of faith and depictions of authority, respectively. Meanwhile, the Cross-Carpet Page from the Lindisfarne Gospels incorporates motifs into Christian art and the Icon of Christ from St. Catherine's Monastery at Mount Sinai, surviving iconoclasm, becomes more of a private object of worship rather than a primarily teaching piece. Therefore, the Dura Europos painting is the most straightforwardly didactic among the listed works.