Sloppy cut-n-paste error using -o, so this is obviously wrong ...

day=`date +%d`
if [ $day -ge 8 -o $day -le 14 ]; then
    echo '2nd Friday'

   # do F2
elif [ $day -ge 15 -o $day -le 21 ]; then
    echo '3rd Friday'

   # do F3
fi

maybe something more like this:

day=$(date +%d)
[[ $day -le 7 ]] && echo "1st Friday" && do_F1 && exit
[[ $day -ge 8 && $day -le 14 ]] && echo "2nd Friday" && do_F2 && exit
[[ $day -ge 15 && $day -le 21 ]] && echo "3rd Friday" && do_F3 && exit
[[ $day -ge 22 && $day -le 28]] && echo "4th Friday" && do_F4 && exit

-Bob