The real "trick" is to get the regex right that extracts the values from $a and $b. One way is:

#!/usr/bin/perl -w
use strict;

my @names = qw( FLY_ABC123_01.jpg 
                PG_ABC123_03.jpg
                SPL_ABC123_02.jpg );
                             
@names = sort{  (my $A) = ($a =~ /.*_(\w+)/);
                (my $B) = ($b =~ /.*_(\w+)/);
                      $A <=> $B
             }@names;
              
print "@names"; 
#prints: FLY_ABC123_01.jpg SPL_ABC123_02.jpg PG_ABC123_03.jpg
[download]

Update:(\d+) is fine here instead of (\w+) as per suggestion from AnomalousMonk