Sumif or Sumifs with date range

Hi all,
Just wanted to know if its possible to use sumif or sumifs with a date range.

Basically, I want to lookup a name in a random list, count the days that they have, and then filter how many of those days fall within a date range.

I've used sumif to lookup the name and count how many days they have in the entire list, but I can't for the life of me figure out how to then see how many of those days fall within specific dates.

Any help would be appreciated.

Ive attached a sample if that helps.

Seems to have done the trick.

Thanks