Which is correct?
I would like to request you to refrain from shouting.
I would like to request of you to refrain from shouting.
I would like to request from you to refrain from shouting.
The simple answer is that it varies. You can:
Request [a person] to [do something]~ 'request visitors to remove their shoes'
Request to have [a thing or a favour]~ request to have his telephone upgraded'
Request for [a thing or favour] ~ 'a request for a new computer'
Request that [something happens] ~ 'request that you refrain from shouting'