Correct spelling, explanation: went is an irregular past tense of the verb to go. The word may seem unrelated, but this is the case for many irregular verbs, so it’s best to learn them by heart. In this case, went is not made by adding a past-tense suffix -ed, as usual, but is derived from an Old English word wend.

Definition of went:
verb, past tense of go
1. to move or proceed to do something
I was bored on Sunday, so I went to the cinema and had a lot of fun.
I went to bed late, and now I’m sleepy.
Everything went according to plan.
2. to leave a place (usually: went out)
I became irritated so I went out without telling anyone.

Incorrect spelling, explanation: whent would be pronounced the same as went, which may be confusing when hearing it, but if we look at the structure of this word, it’s oddly similar to an adverb when. Went, however, as a past tense of go, is derived from an Old English word wend, and there is no reason to insert h there, especially if it doesn’t serve any purpose.