If the participation rate is 60% and 200 million people 16 years or older are not in the labor force, it means that 200 million corresponds to 40% of people 16 years or older. Since 60% of people 16 years or older are in the labor force, the total number of people in the labor force is given by:
300 million people are in the labor force in this economy.
This strategy works because if you subtract one number from another the sum of the two numbers should be the that is being subtracted from. (In this case, it's 200)