Hello Jirka, will all the dates be within a single year or do you want to look for different dates within August in different years? If it's the former then try this formula

=SUM(IF(FREQUENCY(IF(MONTH(Input!B15:B2000)=8;DAY(Input!B15:B2000));ROW(INDIRECT("1:31")));1))

note that column C isn't required....