It should be "explain yourself"
You could add the suffix D. -er to the verb hate in order to convert it into a noun. When you do that, you get the word hater, which is a noun denoting a person who hates. Technically, C is also correct, because you get a noun hating, which is the act of hating - but if you have to choose just one, I'd go with D. When you add -d you get an adjective hated, and when you add -s, you get a verb hates.
