In different cases is an adverbial phrase modifying the "verb accomplish." It should be set off by commas before and after, (that, in different cases, managers) or else the comma should be deleted. If you move the phrase to the end of the sentence the meaning is a little clearer:
Kotler acknowledged (that managers accomplish several activities within the marketing in different cases.) [subordinate clause, direct object of the verb acknowledged.
By the way, I'm not sure what "accomplish several activities within the marketing" means. Perhaps it's clearer in context.
The comma is appropriate, some might even say needed, to separate the opening phrase from the rest of the sentence. However, "the marketing" doesn't work. You could either say simply, "marketing," without the "the," or use "the marketing X," where "X" is a word such as "branch," "department" or "function."