class :

public class ContactTriggerHandler 
{
    private Map<Integer,Integer> mapTimeToTimeOfDay = new Map<Integer,Integer>{6 => 1, 7 => 1, 8 => 1, 9 => 2, 10 => 3, 11 => 4,
                                                                                12 => 5, 13 => 6, 14 => 7, 15 => 8, 16 => 9, 17 => 10, 18 => 11
                                                                                };
    

    public ContactTriggerHandler()
    {
        
    }
    
    public void onBeforeInsert(List<Contact> lstNewContact)
    {
        populateTimeOfDay(new Map<Id, Contact>(), lstNewContact);
    }
    
    public void onBeforeUpdate(Map<Id, Contact> mapOldContact, Map<Id, Contact> mapNewContact)
    {
        populateTimeOfDay(mapOldContact, mapNewContact.values());
    }
    
    private void populateTimeOfDay(Map<Id, Contact> mapOldContact, List<Contact> lstNewContact)
    {
        Integer intHour;
        for(Contact objContact : lstNewContact)
        {
            system.debug('====objContact.date_time_of_call__c==='+ objContact.date_time_of_call__c.hour());
            
            /**On insert 
             * OR
             * On update but if only date_time_of_call__c is changed.
             * **/
            if( objContact.date_time_of_call__c != null 
                    && 
                    (
                        Trigger.isInsert 
                            || 
                        (Trigger.isUpdate && objContact.date_time_of_call__c != mapOldContact.get(objContact.Id).date_time_of_call__c)
                    )
                )
            {
                 intHour = objContact.date_time_of_call__c.hour();
                 
                 if(mapTimeToTimeOfDay.containsKey(intHour))
                 {
                     objContact.Time_of_day__c = mapTimeToTimeOfDay.get(intHour);
                 }
                 
                 // after 7PM or before 6AM ====> 12
                 else if(intHour > 18 || intHour < 6)
                 {
                     objContact.Time_of_day__c = 12;
                 }
                 else
                 {
                     objContact.Time_of_day__c = null;
                 }
                 
            }
            else if(objContact.date_time_of_call__c == null)
            {
                objContact.Time_of_day__c = null;
            }
        }
    }
    
}

trigger ContactTrigger on Contact (before insert, before update) 
{
    ContactTriggerHandler objHandler = new ContactTriggerHandler();
    
    if(Trigger.isBefore)
    {
        if(Trigger.isInsert)
        {
            objHandler.onBeforeInsert(Trigger.new);
        }
        else if(Trigger.isUpdate)
        {
            objHandler.onBeforeUpdate(Trigger.oldMap, Trigger.newMap);
        }
    }
}