I agree with your answer, Ahmed_btm, though I can't say I find the "model answer" to be the most natural here. I would not naturally say, "He admitted breaking the plate."
I would naturally say, "He admitted to breaking the plate." Thus, if I had to choose a "model answer" to the question among the listed choices, I'd choose (c). If I used V-ing immediately after "admitted," I would use the perfective:
(e) Karim admitted having broken the plate and said he was sorry.
That would be a far better model answer, but it is not even listed as an option on your test. If you Google "admitted breaking" versus "admitted having broken," you'll see that the latter is much more common. Here's another GREAT option:
(f) Karim admitted (that) he had broken the plate and said he was sorry.