There are many ways to do this trick, but they all depend on pulling out the sort key (in this case the second column). A simple way for small quantites of data is to use a hash:

use strict;
use warnings;

my %data;

while (<DATA>) {
     my $key = /^\d+\s+(\d+)/ ? $1 : next;
     
     $data{$key} = $_;
}

print $data{$_} for sort keys %data;

__DATA__
77876    8543    CA84985    54E
77873    8003    CA84985    54E
77875    7725    CA84985    54E
77872    8511    CA84985    54E
77873    8123    CA84985    54E
77822    9908    CA84985    54E
77819    8503    CA84985    54E
77826    8040    CA84985    54E
77822    7874    CA84985    54E
77884    8543    CA84985    54E
77809    7211    CA84985    54E
[download]

Prints:

77809    7211    CA84985    54E
77875    7725    CA84985    54E
77822    7874    CA84985    54E
77873    8003    CA84985    54E
77826    8040    CA84985    54E
77873    8123    CA84985    54E
77819    8503    CA84985    54E
77872    8511    CA84985    54E
77884    8543    CA84985    54E
77822    9908    CA84985    54E
[download]