For future questions, don’t post images of data. Instead, use a service like dbfiddle. I’ll anyhow add a sketch for an answer, with a better-prepared question you could have gotten a complete answer. Anyhow here it goes:
-- extrema is the least and the greatest date in staff table
with extrema(mn, mx) as (
select least(min(hired),min(retired)) as mn
, greatest(max(hired),max(retired)) as mx
from staff
), calendar (dt) as (
-- we construct a calendar with every date between extreme values
select mn from extrema
union all
select dateadd(day, 1, d)
from calendar
where dt < (select mx from extrema)
)
-- finally we can count the number of employed people for each such date
select dt, count(1)
from calendar c
join staff s
on c.dt between s.hired and s.retired
group by dt;
If you find yourself doing this kind of calculation often, it is a good idea to create a calendar table. You can add other attributes to it such as if it is a day of in the middle of the week etc.
With a constraint as:
CHECK(hired <= retired)
the first part can be simplified to:
with extrema(mn, mx) as (
select min(hired) as mn
, max(retired) as mx
from staff
),