We use the word ‘ manage ’ as a verb because it indicates the action of controlling or supervising over commodity. 
The word ‘ manage ’ has been deduced from the Latin word- Manus. 
Now, let’s decrypt the meaning of the given options to find their noun form- 
Option A- ‘ Management ’ is a noun that is used to indicate the administration or branch of an association that deals with or controls the effects. Example- I'll report this incident to the operation. ‘ operation ’ is the noun form of the verb ‘ manage ’. So, it's the correct option. 
Option B- ‘ directorial ’ is an adjective that's used to describe the chops or rates needed to be hired as a director. Example- He has been studying and preparing for the directorial post. ‘ directorial ’ isn't the noun form of the verb ‘ manage ’. Hence, it's an incorrect option. 
Option C- ‘ Managing ’ is a verb that's used to denote the action of supervising or controlling effects.Example- She has been managing the accounts department for times. ‘ Managing ’ isn't the noun form of the verb ‘ manage.’ Hence, it's an incorrect option. 
Option D- ‘ Manageable ’ is an adjective that's used to describe a commodity that's attainable or reasonable. Example- She only takes up tasks that are manageable. ‘ Manageable ’ isn't the noun form of the verb ‘ manage ’. Hence, it's an incorrect option. 
Hence, option A is the correct answer.