Lets see.

perl uses what is called a zero-origin, columns are numbered starting at zero, ie 0,1,2,3 so what you considered the 3rd column via $slots_used += (split(/\s+/,$_))[3]; is actualy the 4th column.

when you split via  split(/\s+/,$_) you only split on whitespaces, but it seems you also need to split column 3 by the slash to get what you want.

Just out of cleanness you probably should have chomped your input to get rid of the newline

And it probably makes sense to get rid of the squiggly braces too

use strict; use warnings; 
my %namesum; 
while (my $line=<DATA>) { 
  chomp $line; 
  next unless $line; 
  $line=~s/[\{\}]//g; 
  my @parts=split(/\s+/,$line); 
  my ($slots_used,$slots_free)=split('/',$parts[2]); 
  my $name=substr($parts[0],0,3);
  $namesum{$name}[0]+=$slots_used; 
  $namesum{$name}[1]+=$slots_free; 
  } 

for my $key (sort keys %namesum){ 
  print "\nname:".$key."\n";
  print "total slots used:".$namesum{$key}[0]."\n";
  print "total slots free:".$namesum{$key}[1]."\n";
  } 

__DATA__

{asf192lin1 C 0/8 0 0 0 4503 16 2922 44316 1}
{asf256lin10 + 2/16 15 0 0 4641 16 2926 194108 0}
{cad192lin1 C 0/12 2 0 0 1432 12 3397 179605 0}
{cas256lin1 C 0/12 50 0 56 3992 12 3397 165099 0}
{cas192lin11 C 0/12 50 0 56 3992 12 3397 165099 0}


{dsf192lin6 + 0/16 0 0 0 4751 16 2930 179123 0}
[download]

result

name:asf
total slots used:2
total slots free:24

name:cad
total slots used:0
total slots free:12

name:cas
total slots used:0
total slots free:24

name:dsf
total slots used:0
total slots free:16
[download]

So tell the truth now, was this course homework?