Correct spelling, explanation: went, past tense of go, is an irregular verb. It’s based not on a typical derivation of past tense verbs – by adding the suffix -ed to the base word – but is taken from an Old English word wend, and modified to modern spelling.

Definition of went:
verb, past tense of go
1. to proceed to do something, often involving movement
I went on a trip to Japan and it was amazing.
The party went well despite a few organizational problems.
We couldn’t decide on whether to get popcorn or nachos, so we went with both.
2. to leave a place
Everyone in the room seemed to ignore me, so I just went out without telling anyone I’m leaving.

Incorrect spelling, explanation: whent is a misspelling of went, probably based on an assumption that there might be a silent h, like in some other English words. In this case, however, the base word is not when or where, but wend, so there is no need or reason to add a silent h, as this spelling is very confusing.