MySQL 8.0

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CREATE TABLE mytable(
   Name  VARCHAR(7) NOT NULL 
  ,OrderID INTEGER  NOT NULL
  ,Goods VARCHAR(9) NOT NULL
  ,Date  DATE  NOT NULL
);
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Michael',1,'Shoes','2019/04/05');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Michael',2,'Groceries','2019/05/28');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Michael',3,'Caps','2019/03/02');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Lucas',4,'Shoes','2019/02/28');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Lucas',5,'Caps','2019/03/31');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Mary',6,'Shoes','2018/04/22');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Mary',7,'Shoes','2018/03/25');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Mary',8,'Groceries','2017/08/22');
INSERT INTO mytable(Name,OrderID,Goods,Date) VALUES ('Mary',9,'Caps','2019/01/01');
delete t
from mytable t
inner join (
	select name, min(date) min_date 
	from mytable 
	where goods = 'Shoes' 
	group by name
) t1 on t.name = t1.name and t.date > t1.min_date
select * from mytable


Name
OrderID
Goods
Date


Michael
1
Shoes
2019-04-05

Michael
3
Caps
2019-03-02

Lucas
4
Shoes
2019-02-28

Mary
7
Shoes
2018-03-25

Mary
8
Groceries
2017-08-22

Name	OrderID	Goods	Date
Michael	1	Shoes	2019-04-05
Michael	3	Caps	2019-03-02
Lucas	4	Shoes	2019-02-28
Mary	7	Shoes	2018-03-25
Mary	8	Groceries	2017-08-22