I don't see how the code you posted is relevant. You can use arithmetic on seconds if you don't care about timezones, daylight saving times, leap seconds etc.

#! /usr/bin/perl
use warnings;
use strict;

use Time::Piece;


my $last_modified = 'Time::Piece'->strptime('2015-05-20 03:52:13', '%Y
+-%m-%d %H:%M:%S');
my $diff = -($last_modified - localtime) / 60 / 60;
print $diff < 12 ? 'less' : 'more (or equal)', " than 12 hours\n";
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See also DateTime and Date::Manip.