How labor coefficients are calculated to find out the manpower requirement for a particular activity?

There is no direct formula for that. Getting the resource requirement would greatly depend on the type of activity and the tasks required on those activities.  The resource factor depends on what kind business vertical you are into.  You also need to consider risk factors and availability factors.

There's more to it in resource management that just putting a standard computation.  Always remember, an activity consist of three types of resources: human resource, equipment resource and material resource. Figuring out how much is required depends on your plan