What tactical mission task involves breaking through an enemy's lines?

The tactical mission task that involves breaking through an enemy’s lines is breaching. This task is specifically designed to create gaps in enemy defenses, allowing friendly forces to penetrate and exploit these weaknesses. A breach operation often requires specialized equipment and techniques, as it's crucial for overcoming obstacles such as fortifications or minefields that the enemy has put in place to defend their position.

In contrast, seizing typically refers to taking control of key terrain or objectives without the specific emphasis on penetrating defenses. Defeating suggests a broader operational goal of rendering an enemy force ineffective, which can involve various tactics beyond just breaking through lines. Destroying generally involves annihilating enemy forces or assets but does not specifically encapsulate the action of penetrating a defensive position as breaching does. Thus, the focus on creating an avenue for advance against enemy forces makes breaching the most accurate answer in this context.