The correct answer is: A. Explaination
The correct spelling of the word is "explanation".
The word "explaination" is not a word in the English language. The correct spelling is "explanation". The word "explanation" is a noun that means the act of explaining something or the fact of being explained. It can also mean a statement that explains something.
The word "explaination" is often misspelled because it sounds like the word "explanation". However, the two words are not spelled the same. The word "explaination" is not a word in the English language, so it should not be used.
The other three words in the question are spelled correctly. The word "extermination" means the act of destroying something completely. The word "exaggeration" means an overstatement of something. The word "expectation" means a belief that something will happen.