From reading posts so far, I take it that the Monks are irritated that you haven't presented any attempts at code of your own. Giving an attempt yourself is an important part of the learning process. The Monks will grow deaf to your requests if you don't start writing code yourself!

Comparing dates/times can get complicated. In general, I recommend converting input strings to output strings in ISO format 3. This is like "YYYY-MM-DD" where leading 0's are required for single digit fields. The reason for doing this is that you can use a string comparison or simple sort rather than a more complex numeric sort. Here is some code for you. Note that I use string comparisons of "ge" (greater than or equal) and "le" (less than or equal).

Update: Minor code improvement to if statement, deleted $_ from print $_ as that is extraneous.

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

my $start ='2018-02-03';  #ISO 3 format YYYY-MM-DD
my $end   ='2018-02-06';

while (<DATA>)
{
   if (my ($day, $month, $year) = $_ =~ m/(\d{2})\/(\d{2})\/(\d{4})\s*
+$/)
   { 
      my $this_date = "$year-$month-$day";
      print if ($this_date ge $start and $this_date le $end);
   }
}   

=prints
K20TQ67   K1L0V       T6Z148X  111.222.333.123 HOME - [03/Feb/2018:01:
+08:39 -0800]              03/02/2018
SO78NZ28   B5S8J       W9F920Z  111.222.333.123 HOME - [04/Feb/2018:01
+:08:39 -0800]          04/02/2018
BI55SY64   R6P5H       A9U757R  111.222.333.123 HOME - [05/Feb/2018:01
+:08:39 -0800]              05/02/2018
ET43US76   F5S3W       X2L870O  111.222.333.123 HOME - [06/Feb/2018:01
+:08:39 -0800]              06/02/2018
=cut


__DATA__

some bogus line here
DQ94JD84   S8G2H       A9X946N  111.222.333.123 HOME - [01/Feb/2018:01
+:08:39 -0800]              01/02/2018
XA29EN35   M4C6M       D7F577Q  111.222.333.123 AWAY - [02/Feb/2018:01
+:08:39 -0800]        02/02/2018
JK20TQ67   K1L0V       T6Z148X  111.222.333.123 HOME - [03/Feb/2018:01
+:08:39 -0800]              03/02/2018
SO78NZ28   B5S8J       W9F920Z  111.222.333.123 HOME - [04/Feb/2018:01
+:08:39 -0800]          04/02/2018
BI55SY64   R6P5H       A9U757R  111.222.333.123 HOME - [05/Feb/2018:01
+:08:39 -0800]              05/02/2018
MH72RG27   Y6X0N       C7E352J  111.222.333.123 HOME - [01/Feb/2018:01
+:08:39 -0800]                    01/02/2018
ET43US76   F5S3W       X2L870O  111.222.333.123 HOME - [06/Feb/2018:01
+:08:39 -0800]              06/02/2018
QA43MM82   Y3K0O       H8E229P  111.222.333.123 HOME - [11/Feb/2018:01
+:08:39 -0800]        11/02/2018
MK72HI41   A6W2I       M3X402D  111.222.333.123 HOME - [15/Feb/2018:01
+:08:39 -0800]        15/02/2018
LJ28XY72   E0Z4L       E8W757S  111.222.333.123 HOME - [22/Mar/2018:01
+:08:39 -0800]          22/03/2018
TJ47EG77   W5J6A       A7L557Q  111.222.333.123 HOME - [01/Feb/2018:01
+:08:39 -0800]              01/02/2018
TJ47EG78   E6L8Z       J4X329P  216.142.233.73 - - [30/Nov/2018:00:03:
+08 -0500]              30/11/2018
TJ47EG79   N2V1H       Q1Y615G  10.101.128.66 - - [03/Apr/2018:00:42:1
+1 -0500]                03/04/2018
[download]

I don't know where the trailing, 22/03/2018 stuff came from? It appears that [03/Apr/2018:00:42:11 -0500] is the real time stamp. The -0800 means 8 hours behind GMT or UTC (perhaps Pacific Standard Time?). Yes, there is a fine difference between GMT and UTC that is meaningless here. Typically what would be done here is convert these times into UTC and use that for all DB storage. Convert to local time like perhaps Pacific Daylight Savings Time which is -0700 from GMT for user presentation.