The original question was not referring to regulations, else this would be much simpler.
on a non ETOPs route for a twin engine operation what's the weather requirements for an enroute alternate airport, as far as I remember there's no requirement but I cannot find where it would be written
and is there any difference for this rule for a 4 engine operation
He is looking for a requirement, and with the reference to the difference for four engine aircraft, it is easy to assume that he's referring to Air Carrier Operations. In which case, the FOM supersedes the Regulations PROVIDED that they are more restrictive than the applicable Reg. If I assumed his question correctly, his companies FOM is the approved source for requirments, thus the answer lies there.
I looked in three separate FOM's from other Air Carriers and found very similar requirements.
Otherwise, the only clearly stated "Regulation" is that from the US FAA (FAR121), which ONLY applies to Air Carriers. FAR 91 (General Aviation) does not include such a requirement.