You have 2 StrToDate() calls in that highlighted code (presumably more offscreen?), both are converting scGPDBDateEdit11.Text. Your earlier screenshot show the Text is ' / / ', which is obviously NOT a valid date string, which is why StrToDate() raises EConvertError.
It should work just fine, eg:
if TryStrToDate(scGPDBDateEdit11.Text, mydate) then begin
// use mydate as needed...
end else begin
// do something else...
end;
Though, like I said, TDateTimePicker makes a lot more sense then a TEdit for date inputs, eg:
mydate := IncYear(DateTimePicker11.Date, a);
...
mydate := IncDay(DatePicker11.Date, a);
...