What is the best method for allocating Manufacturing O.H of services cost centers to production cost centers and justify your answer?

That depends on the product in question. Indirect production cost is uaually allocated using the highest valued item in the product's cost structure. This might be time, weight, count, direct manpower's cost, raw material cost, etc.....

To my understanding of the question, the best method here is to use hours volume of each production section in a way to allocate costs to every stage of production . the section which worked more gets more cost of services.