This is a difficult question to answer because it is more a question of style than a question of grammar.
The first option is the worst. "Thorough" is an adjective. It is not a suitable modifier for a verb. One way or another, you should use the adverb "thoroughly". As I judge these options, this is the only one with bad grammar.
The last option is a split infinitive. Old-fashioned style guides recommend (or even demand) that you avoid split infinitives. Personally, I find this to be a good option. I cannot speak for whatever style guide you might be required to follow.
The remaining option avoids the split infinitive, but it poses a different stylistic problem. It places the adverb between the infinitive and its object. I have to recommend that you avoid that. I have no idea whether your style guide considers that to be a problem.
The best option is an option that you don't list. Place the adverb after the infinitive's direct object:
It is essential to clean the machine thoroughly after each use.
However, on a multiple choice test, you cannot choose an option which is not provided.