SQL Server 2019

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Microsoft SQL Server 2019 (RTM-CU3) (KB4538853) - 15.0.4023.6 (X64) Mar 4 2020 00:59:26 Copyright (C) 2019 Microsoft Corporation Express Edition (64-bit) on Windows Server 2019 Standard 10.0 <X64> (Build 17763: ) (Hypervisor)

declare @tab table (Mode int, StartDate varchar(10), EndDate varchar(10))
insert into @tab select 0, '1/1/2018',  '1/12/2018'
insert into @tab select 0, '1/5/2015',  '1/12/2018'
insert into @tab select 0, '3/8/2015',  '1/12/2019'
insert into @tab select 0, '1/1/2020',  '1/1/2020'
insert into @tab select 0, '5/5/2015',  '5/5/2015'
insert into @tab select 1, '1/1/2018',  '5/5/2015'
insert into @tab select 1, '5/8/1947',  '9/9/1902'
insert into @tab select 1, '4/4/2014',  '3/3/2013'
insert into @tab select 1, '1/4/2020',  '1/1/2001'
insert into @tab select 1, '3/8/2015',  '1/12/2019'
insert into @tab select 1, '19/11/1992','19/11/1992'

;with cte as 
(
	select Mode, StartDate, EndDate, ROW_NUMBER() over (partition by Mode, case when CONVERT(date, StartDate, 103) < CONVERT(date, EndDate, 103) then 0 when CONVERT(date, StartDate, 103) = CONVERT(date, EndDate, 103) then 1 else 2 end order by Mode) rn
	from @tab
)

select Mode, StartDate, EndDate from cte 
where rn = 1
order by Mode,  CONVERT(date, StartDate, 103)

Mode	StartDate	EndDate
0	1/1/2018	1/12/2018
0	1/1/2020	1/1/2020
1	19/11/1992	19/11/1992
1	3/8/2015	1/12/2019
1	1/1/2018	5/5/2015