。
She has a good grasp of her homeroom class.
Literal
She [topic-は] homeroom [genitive-の] class [object-を] well is-grasping.
把握する ('to grasp / understand fully') is a common Sino-Japanese compound used metaphorically for understanding situations, data, or — as here — the dynamics of a group. Note that 担任のクラス here means 'the class she teaches' (the class for which she serves as 担任), not 'the homeroom class she is a member of'; with a teacher subject, the possessive flips to the supervised group. The ~ている marks her ongoing state of having a grasp on it (resultative).