Hi Eldon, here is the code 

//Task Trigger
if(trigger.isAfter)
    {
        if(trigger.isInsert || trigger.isUpdate)
        { 
             RelatedTask.method1(trigger.new);
         }
}
//Task Class: RelatedTask
public static void method1(List<Task> taskRecords){   
try{
      
        List<Task> listTsk=new List<Task>();
        List<Contact> listCont=new List<Contact>();
        List<String> tskGrpName=new List<String>();    
        List<Id> taskWhatId=new List<Id>();
        List<Task> accountTasks=new List<Task>();
       
        for(Task tsk:taskRecords)
        {
            String taskgr=tsk.Account_Group_Task__c;
            Id taskleadId=tsk.WhoId;
                                   
            // if(wId!=null && wId.startsWith('001') && !listTask.contains(tsk.WhatId))
            if(taskgr!=null)
            {   
                tskGrpName.add(tsk.Account_Group_Task__c);
            }             
           
             if(tsk.WhatId!=null)
             {
                 taskWhatId.add(tsk.WhatId);
             }
           
        }                                                   
		
      
listTsk= [SELECT Id, ActivityDate,WhatId,WhoId,Primary_Contact__c,Status,Meeting_Purpose__c,Type,Account_Name__c,
RecordTypeId,Account_Group_Task__c,Last_meeting_90_days__c,Next_meeting_90_days__c FROM Task Where Account_Group_Task__c IN : tskGrpName AND (RecordTypeId=:Account_Activity_RECORD_TYPE_ID OR RecordTypeId=:Opportunity_Activity_RECORD_TYPE_ID) AND (Meeting_Purpose__c='Executive' OR Meeting_Purpose__c='Operational')  AND Status='Completed' AND (Type='F2F' OR Type='Call') Order by ActivityDate];
              
        Map<Id, Account> accMaps=new Map<Id, Account>([Select Id,Last_Onsite_Activity_A_T__c,Last_Remote_Activity_A_T__c,Name from Account Where Id IN:taskWhatId]);
            
     
        Map<Id, Opportunity> oppMaps=new Map<Id, Opportunity>([Select Id,Last_Onsite_Activity_O_T__c,Last_Remote_Activity_O_T__c from Opportunity where Id IN:taskWhatId]);    
                
        Map<Id, Account> actn = new Map<Id, Account>();
        Map<Id, Opportunity> opps = new Map<Id, Opportunity>();
     
        for(Task tk:listTsk)
        {   
            if(tk.Type=='F2F')
            {
               if(accId!=null)
                {  System.debug('Account Name is ' + accId.Name);
                        System.debug('Task Type ' +tk.Type);
                   		 if(tk.WhatId==accId.Id)
                			{
                   				accId.Last_Onsite_Activity_A_T__c=tk.ActivityDate;
                			}
                 }
                else if(oppId!=null)
                 {
                     if(tk.WhatId==oppId.Id){
                     oppId.Last_Onsite_Activity_O_T__c=tk.ActivityDate;
                 } 
					}
            }
            if(tk.Type=='Call')
            {
             if(accId!=null)
                {  System.debug('Account Name is ' + accId.Name);
                      System.debug('Task Type ' +tk.Type);
                   		 if(tk.WhatId==accId.Id)
                			{
                                accId.Last_Remote_Activity_A_T__c=tk.ActivityDate;
                			}                            
                    }
                else if(oppId!=null)
                {
                    if(tk.WhatId==oppId.Id){
                     oppId.Last_Remote_Activity_O_T__c=tk.ActivityDate;
                                System.debug('Opp Last Remote Activity ' +  oppId.Last_Remote_Activity_O_T__c);
                 }
                }
            }
             }
        update oppMaps.values();
        update accMaps.values();
        
   
    } catch(DmlException de)
    {
        System.debug('Error While Executing '+ de.getLineNumber());
    }
}
----------------------------------------------------------------------------------------------------------------
//Opportunity Trigger
if(trigger.isAfter)
    {    
        if(trigger.isUpdate)
        {
          CustomOpportunity.findRecentActivityDate(trigger.new);  
        }
    }


//Opportunity Class : CustomOpportunity
public static void findRecentActivityDate(List<Opportunity> opptys)
    { 
  try{
        List<Opportunity> listOpp=new List<Opportunity>();
        Set<Id> oppIds=new Set<Id>();
        Set<Id> accIds=new Set<Id>();
        List<String> accountGroupId=new List<String>();
        for(Opportunity ops:opptys)
        {
            oppIds.add(ops.Id);
            accIds.add(ops.AccountId);
            accountGroupId.add(ops.Account_Group_Id_Opp__c);
        }

        Map<Id, Opportunity> oppsOnsite=new Map<Id, Opportunity>([select Id,AccountId,Last_Onsite_Activity_O__c,Last_Remote_Activity_O_T__c from Opportunity where Account_Group_Id_Opp__c IN:accountGroupId Order by Last_Onsite_Activity_O__c Desc Limit 1]);

        Map<Id, Opportunity> oppsRemote=new Map<Id, Opportunity>([select Id,AccountId,Last_Onsite_Activity_O__c,Last_Remote_Activity_O_T__c from Opportunity where Account_Group_Id_Opp__c IN:accountGroupId Order By Last_Remote_Activity_O_T__c Desc Limit 1]);
       
 Map<Id, Account> accnts= new Map<Id, Account>([Select Id, Last_Onsite_Activity_A_O__c,Last_Remote_Activity_A_O__c from Account where Id IN:accIds]);
     
        for(Opportunity opp : oppsOnsite.values())
        {
	        Account accId=accnts.get(opp.AccountId);
            accId.Last_Onsite_Activity_A_O__c=opp.Last_Onsite_Activity_O__c;
        }

    	for(Opportunity opp1:oppsRemote.values())
        {
            Account accId1=accnts.get(opp1.AccountId);
            accId1.Last_Remote_Activity_A_O__c=opp1.Last_Remote_Activity_O_T__c;
        }
       update accnts.values();
     }
Catch(DMLException de)
        {
            System.debug('Error While Executing ' + de.getLineNumber());
        }
    }