Hi,

I can writte trigger like this.

public class PopulateData{
public static void changeData(List<Commission_line__c> comList){
 set<id> commissionRateSet=new set<id>();
    for(Commission_line__c com:comList){
        commissionRateSet.add(con.account__c);
    }
  List<Commission_rate__c> commissionRateList=new List<Commission_rate__c>([select id,Rate__c from Commission_rate__c where id in: commissionRateSet]);
    
    List<Commission_line__c> CommissionlineList=new List<Commission_line__c>();
    for(Commission_rate__c cmr:commissionRateList){
        for(Commission_line__c com:comList){
            if(cmr.id==com.account__c){
            
            if(com.category__c=='hardware' && com.CloseDate__c==date.newinstance(2021, 4, 15)){
                Commission_line__c comInstance=new Commission_line__c();
                comInstance.id=com.id;
                comInstance.Rate__c=cmr.Rate__c;
                CommissionlineList.add(comInstance);
            }
               
            }
        }
    }
    
    update CommissionlineList;

}
}

trigger

trigger ContactTrigger on Commission_line__c (after undelete, before delete,After Insert,before insert,before update) {
if(trigger.isAfter && trigger.isInsert){
	PopulateData.changeData(trigger.new);
}

here is the case Commission_line__c is a child and Commission_rate__c is a parent.
If it helps you please mark it as The Best Answer.

Thank You