开课 is a separable verb (离合词). It has two main meanings: (1) for a school, to begin classes after a break (e.g., 学校下周开课 'school starts next week'); (2) for a teacher, to offer or teach a course (e.g., 他这学期开了三门课 'he is offering three courses this semester'). When you need to insert a measure word, duration, or object, split it: 开 + (了/过/着) + (number + classifier) + 课. Do not confuse with 上课 (shàng kè 'to attend class'), which is from the student's perspective.