You don't need to loop through the hash for every line of file 2. Just check if the hash key exists. Try something like this:

#!/usr/bin/perl -w

use strict;

my $phi = `ls slk`;
my $phi2 = `ls *.csv`;
chomp($phi);
chomp($phi2);

open(OUT,"> /home/Aug18.csv") or die "Cannot open output file;
open(READDATA, "< /home/$phi") or die "Cannot Open file;

my %h;
while (my $stuff = <READDATA>){
  if ($stuff =~ /(\d\d\d\d\w\d?)\s+(\w*)/){
    $h{$1} = $2;
  }
}
close READDATA;

open(READDATA2, "< /home/$phi2") or die "Cannot Open file.;
while (my $stuff2 = <READDATA2>){
  chomp($stuff2);
  if (exists $h{$stuff2}){
    print OUT "$stuff2,$h{$stuff2}\n";
  }
}
close READDATA2;
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