。
She has firm command over her homeroom class.
Literal
She [topic-は] homeroom [genitive-の] class [object-を] well is-commanding.
Identical structure to the 把握 sentence but a sharper meaning: 掌握 ('grasping in the palm') is more authoritative than 把握 ('mental grasp') — it implies firm control, not just understanding. 把握 is what an analyst does to data; 掌握 is what a leader does to people, territory, or power. Common in business and political contexts (権力を掌握する 'seize power'), and a strong word to apply to a teacher — it suggests not just understanding her class but commanding it.