IF with multiple conditions

[AnneUSA]

I sent the entire morning trying to figure this one out, it's time to recognize I need help
I am trying to figure out how many client days we are accruing each month but I don't know how to include multiple conditions properly into my formula.

F8 = whether a client stayed at a certain location or not.
C$3 and B$3 are dates (first day of the month, last day of the month)
K8 is the date the patient left (if he/she left during the month)
IF F8=''','''' OTHERWISE IF C$3<K8>B$3, K8-C$3 OTHERWISE IF K8="", B$3-C$3

I have attached the spreadsheet. Help!!

thanks!

Anne