Correct spelling, explanation: without comes from Middle English withouten and is a combination of two prepositions: with and out, which perfectly describe its meaning. A blend -ought is pronounced similarly to out, hence the misspelling withought. The only correct form is without.

Definition of without:
preposition, not including something
We are going there without Amanda.
I don’t look good without fringe.
adverb (rare), outside
The weather without is hideous.

Incorrect spelling, explanation: this form is incorrect. It may seem that pronunciation points to such spelling (-ought blend is pronounced similarly to out), but it is wrong. The correct form is without, which derives from Middle English withouten.

Incorrect spelling

Incorrect spelling

Incorrect spelling