Correct spelling, explanation: this word has its roots in Middle English thorow and this may be the reason for its spelling and pronunciation. Throught is a misspelling and may be confused with the archaic use of thorough which is a preposition/adverb through.

Definition of thorough:
1. adjective, something done with a lot of care for details
Next time your research should be much more thorough.
2. adjective, someone who pays attention to details
I like classes with Mr Smith. He is a very thorough professor.
2. (archaic), adverb/preposition, through

Incorrect spelling, explanation: throught is an incorrect form because such a word simply doesn’t exist in English. It is probably mistaken with through which is an old meaning of the adjective thorough. Thorough is the correct spelling and comes from old form thorow.

Incorrect spelling

Incorrect spelling

Incorrect spelling