Why are you struggling with this? It's just a minor scaling problem with dimensional analysis.
Think about each unit fraction and why it may have been included.
circumference of a circle is 15.7inches and object goes around the circle at 6000revs per min. an event occurs ever revolution the event occurs for 3.33 milliseconds and always ends at 23 degrees after top dead center(so 23 degrees in to the new rotation) at the speed the object it traveling (6000revs per min.) at what degree does the event have to start to end at 23 degrees.. also when does the event need to start if the speed is 700 revs per min.