MySQL 8.0

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select version();


version()


8.0.23


create table tableA (Units int, Date date);
insert into tableA values
(32,"2021-01-01"),
(37,"2021-02-01"),
(47,"2021-03-01");

Create table tableB (StartDate date, EndDate date);
insert into tableB values
("2021-01-15","2021-01-29"),
("2021-01-30","2021-02-12"),
("2021-02-13","2021-02-26"),
("2021-02-27","2021-03-12");
SELECT Units, Date, StartDate, EndDate
  FROM tableA a
  LEFT JOIN tableB b
    ON a.Date<= b.EndDate
    AND MONTH(a.Date) = MONTH(b.EndDate)
    ORDER BY b.StartDate


Units
Date
StartDate
EndDate


32
2021-01-01
2021-01-15
2021-01-29

37
2021-02-01
2021-01-30
2021-02-12

37
2021-02-01
2021-02-13
2021-02-26

47
2021-03-01
2021-02-27
2021-03-12

Units	Date	StartDate	EndDate
32	2021-01-01	2021-01-15	2021-01-29
37	2021-02-01	2021-01-30	2021-02-12
37	2021-02-01	2021-02-13	2021-02-26
47	2021-03-01	2021-02-27	2021-03-12