Countif with multiple AND/OR criteria

[kazphilips]

I'm trying to count how many accounts of a given type appear for a given sales rep. If you see my attachment, B4 needs to show the total number of only the Medcare Company, Inv Lab and Physicians accounts with Extended hours are listed for Andrew Williams on Sheet 2 "Accounts". The formula below doesn't work and I'm not sure why:
=COUNTIF(Accounts!$B:$B,A4)*AND(OR(Accounts!$F:$F="Medcare Company",Accounts!$F:$F="Inv Lab",Accounts!$F:$F="Physicians",Accounts!$H:$H="Yes"))

REP ID countif test.xlsx