SQL Server 2012

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

CREATE TABLE TableA
    ([ID] int, [RequestNumber] int, [Date] datetime)
INSERT INTO TableA
    ([ID], [RequestNumber], [Date])
VALUES
    (1, 1, '2017-09-27 09:30:00'),
    (2, 1, '2018-06-02 09:30:00')
2 rows affected

CREATE TABLE TableB
    ([RequestNumber] int, [Serial] int, [Date] datetime)
INSERT INTO TableB
    ([RequestNumber], [Serial], [Date])
VALUES
    (1, 1, '2017-09-27 09:30:00'),
    (1, 2, '2017-09-27 09:30:00'),
    (1, 6, '2018-06-03 09:30:00'),
    (1, 7, '2018-06-03 09:30:00'),
    (1, 8, '2018-06-03 09:30:00')
5 rows affected

select a.*, b.*
from tablea a cross apply
     (select top (1) with ties b.*
      from tableb b
      order by abs(datediff(day, a.date, b.date))
     ) b


ID
RequestNumber
Date
RequestNumber
Serial
Date


1
1
27/09/2017 09:30:00
1
1
27/09/2017 09:30:00

1
1
27/09/2017 09:30:00
1
2
27/09/2017 09:30:00

2
1
02/06/2018 09:30:00
1
6
03/06/2018 09:30:00

2
1
02/06/2018 09:30:00
1
7
03/06/2018 09:30:00

2
1
02/06/2018 09:30:00
1
8
03/06/2018 09:30:00

ID	RequestNumber	Date	RequestNumber	Serial	Date
1	1	27/09/2017 09:30:00	1	1	27/09/2017 09:30:00
1	1	27/09/2017 09:30:00	1	2	27/09/2017 09:30:00
2	1	02/06/2018 09:30:00	1	6	03/06/2018 09:30:00
2	1	02/06/2018 09:30:00	1	7	03/06/2018 09:30:00
2	1	02/06/2018 09:30:00	1	8	03/06/2018 09:30:00