。
She gave him that task.
Literal
She [topic-は] that work [object-を] him [recipient-に] imposed.
課する (or 課す in some readings) is a formal verb for 'to impose, assign, levy' — used for tasks, taxes, duties, obligations. The pattern [recipient]に + [thing imposed]を + 課する is standard. The verb has a slight authoritative or institutional flavor, fitting workplaces, schools, governments — anywhere obligations are formally assigned. Compare with the more colloquial 押し付ける ('push onto, force upon'), which carries a more negative, unwanted-imposition flavor.