Here is my solution:

declare @test-2 table(

PatientNumber int,

DischargeDate date

);

insert into @test-2

values (1,'2015-11-30'),

(1,'2016-01-01'),

(1,'2016-03-04'),

(1,'2016-05-08'),

(2,'2015-12-02'),

(2,'2015-12-19'),

(2,'2016-02-24'),

(2,'2016-05-28'),

(2,'2016-07-30');

select * from @test-2;

with basedata as (

select

PatientNumber,

max(DischargeDate) DischargeDate

from

@test-2

group by

PatientNumber

)

select

bd.PatientNumber,

ca1.DischargeDate

from

basedata bd

cross apply (select DischargeDate from @test-2 t1 where bd.PatientNumber = t1.PatientNumber and t1.DischargeDate > dateadd(month,-3,bd.DischargeDate)) ca1;