Can a landlord ask the tenant to pack out without any proof that state the tenant to vacate the house even without the tenant oweing the landlord for houserent

This depends entirely on the Lease agreement that has been signed by the Parties. While some lease agreements do not have an escape clause (early termination) in most cases, leases can be terminated by giving the other party sufficient notice to vacate. In this case, it seems that the notice given is ample and the period of 4 months (provided that there is no condition to have premature termination) is sufficient.