Counting unique clients per date/time:
B9: =UNIQUE(Table1[Appt Details])
A9: =COUNT(UNIQUE(FILTER(Table1[Client Number],Table1[Appt Details]=C10)))
Counting unique clients per date:
B13: =UNIQUE(INT(Table1[Appt Details]))
A13: =COUNT(UNIQUE(FILTER(Table1[Client Number],INT(Table1[Appt Details])=C14)))
Assuming that Table1 is A1:B7, with header in first column.