I know we can update contact fields based on account fields by using process builder but can we use trigger for that is it possible?

Try The Following Code

In This When Account Updates CheckBox Field On Contact is Updated
trigger accountcontat on Account (after update){
   List<Contact> contactList = new List<Contact>();
   List<Contact> contactList1 = new List<Contact>();
for(Account acc: [SELECT Id,(SELECT Id,checkbox__c FROM Contacts) FROM Account WHERE Id in: Trigger.new]){
   If(acc.Contacts.size()>0){
     contactList.addAll(acc.Contacts);
    }
}
for(contact c:contactList){
       c.checkbox__c=true;
       contactList1.add(c);
}
update contactList1;
}