You can avoid the dml and soql here by using the standard Trigger.oldMap and Trigger.newMap

Try the below code:

1. trigger TriggerWithEntryCriteria on Account (after update)   
2.     {  
3.             Set<Id> setUpdatedIds = new Set<Id>(); // 1
   
4.             List<Contact> lstContactsToBeUpdated = new List<Contact>(); // 2
   
5.             for(Account acc : Trigger.New)  
6.             {  
7.                if(acc.Fax != Trigger.OldMap.get(acc.Id).Fax)       // 3          
   
8.                     {  
9.                         setUpdatedIds.add(acc.Id);
   
10.                     }  
11.              }
12.              for(Contact c : [Select AccountId, Fax From Contact Where AccountID IN : setUpdatedIds]) // 4
    
13.              {
    
14.                   c.Fax = Trigger.newMap.get(c.AccountId).Fax;
    
15.                   lstContactsToBeUpdated.add(c);
    
16.              }
    
17.             
    
18.              if(lstContactsToBeUpdated.size() > 0) // 5
    
19.                   update lstContactsToBeUpdated;
    
20.  
21.     }

Here,

1 = new set to store those Account Id's whose Fax has been changed.

2 = new list to store contacts that are to be updated (this is to avoid updating each Contact inside the for loop)

3 = checking if the account's fax has been changed. If yes, store it's id in the new set.

4 = Querying all Contacts whose Account's fax has been changed. Assigning the new fax number to each of the associated Contacts

5 = updating the Contacts.

Let me know if you have any doubts.