Well, I have read many above answers and applied them too. Some of them work fine and will allow you to pass the first Challenge but if the correct solution to this is :
 

MaintenanceRequest.apxt

trigger MaintenanceRequest on Case (before update, after update) {
    // ToDo: Call MaintenanceRequestHelper.updateWorkOrders
    Map<Id,Case> mapofMntRque = new Map<Id,Case>();
    if(Trigger.isUpdate && Trigger.isAfter)
    {
        for(Case ca: Trigger.New)
        {
            if(ca.Type.equalsIgnoreCase('Repair') || ca.Type.equalsIgnoreCase('Routine Maintenance') && ca.IsClosed == true)
            {
                mapofMntRque.put(ca.Id, ca);
            }
        }
    }
    if(!mapofMntRque.isEmpty())
    {
        system.debug('Calling MaintenanceRequestHelper.updateWorkOrders');
        MaintenanceRequestHelper.updateWorkOrders(mapofMntRque);
    }
}

MaintenanceRequestHelper.apxc

public with sharing class MaintenanceRequestHelper {
    
    public static void updateWorkOrders(Map<Id,Case> mapofMntRque) {
        // TODO: Complete the method to update workorders
        /*

        This section gives a solution to this bellow statement :
        "Another aspect about parts is they all have different lifespans. Therefore, you need to calculate and set the next due date using the maintenance cycle defined on the related work part records. If multiple work parts are used in the maintenance request, choose the shortest maintenance cycle to define the service date." 

        The above statements are skipped by many of the developers and this also gets skipped by the salesforce validations but I think this is important. It is for knowledge purpose.

        You can comment on this below this till the next comment if errors occur.
        /*

        String query2 = 'select id,(select equipment__r.maintenance_cycle__c from work_parts__r) from case';
        List<Case> CaselistToEquip = database.query(query2);
        Map<Id,Decimal> case2MaintenanceCycle = new Map<Id,Decimal>();
        for(case ce : CaselistToEquip)
        {
            Decimal maintenanceCycle = 0.0;
            for(work_part__c wp : ce.work_parts__r)
            {
                maintenanceCycle = (maintenanceCycle > wp.equipment__r.maintenance_cycle__c) ? wp.equipment__r.maintenance_cycle__c : maintenanceCycle;
            }
            case2MaintenanceCycle.put(ce.id,maintenanceCycle);
        }

        // comment above if errors occur.

        
        List<Case> caseList = new List<Case>();
        
        if(!mapofMntRque.isEmpty())
        {
            for(Case ca : mapofMntRque.values())
            {
                system.debug('------'+ca.Id);
                Case newCa = new Case();
                newCa.Vehicle__c = ca.Vehicle__c;
                newCa.Equipment__c = ca.Equipment__c;
                newCa.Type = 'Routine Maintenance';
                newCa.Subject = (string.isBlank(ca.Subject)) ? ('Routine Maintenance Request') : (ca.Subject) ;
                newCa.Date_Reported__c = date.today();

                // comment next line if error occur.
                newCa.Date_Due__c =  (case2MaintenanceCycle.containsKey(ca.Id)) ? Date.today().addDays(Integer.valueOf(case2MaintenanceCycle.get(ca.Id))) : date.today();

                /* 
                uncomment this section and comment the just the above whole line.

                newCa.Date_Due__c =  (ca.Equipment__r.Maintenance_Cycle__c != null) ? Date.today().addDays(Integer.valueOf(ca.Equipment__r.Maintenance_Cycle__c)) : date.today(); 
                
                */

                newCa.Origin = 'Phone';
                newCa.Status = 'New';
                caseList.add(newCa);
            }
            insert caseList;
        }
    }      
}

If works for you. Mark this the best answer.