# Pull out the numbers of the checkboxes that were selected.
# e.g. If box1, box3 and box12 were selected, @selected = (1, 3, 12)
my @selected = grep { $_=$1 if /^box(\d+)/; } $q->params();

open FH, $filename or die "Can't read $filename, $!";  # open for read
my @posts = <FH>;  

# This should delete the post text associated with each selected checkbox
# You have to use the @selected array in reverse.  I leave the 
# explanation for this as an exercise for you. :)
splice @posts, ($_ - 1), 1 for reverse @selected;

# Now write the file back out again
open FH, ">$filename" or die "Can't write to $filename, $!";
print FH @posts or die "Couldn't write to file, $!";
close FH or die "Can't close file etc, $!";