。
Don't speak to him while he's studying.
Literal
Study is-doing while [topic-は] him [to-に] don't-talk-to.
~ている間 ('while X is happening') pairs the ongoing-action form with the duration noun 間. The pattern specifies a timespan during which something holds. 話しかける ('to speak to, address') is a compound verb (話す + かける), with ~かける adding 'directed toward someone.'