use warnings;
use strict;

my $rtn = [
          {
            'ship_cost' => '80.84',
            'ServiceType' => 'FIRST_OVERNIGHT',
            'ship_note' => 'Overnight Delivery by 8:00 or 8:30 am',
            'ship_tag' => 'First Overnight'
          },
          {
            'ship_cost' => '43.71',
            'ServiceType' => 'PRIORITY_OVERNIGHT',
            'ship_note' => 'Overnight Delivery by 10:30 am',
            'ship_tag' => 'Priority Overnight'
          },
          {
            'ship_cost' => '38.74',
            'ServiceType' => 'STANDARD_OVERNIGHT',
            'ship_note' => 'Overnight Delivery by 3:00 pm',
            'ship_tag' => 'Standard Overnight'
          },
          {
            'ship_cost' => '17.5',
            'ServiceType' => 'FEDEX_2_DAY',
            'ship_note' => '2 Business Days Delivery by 4:30 pm',
            'ship_tag' => 'Fedex 2 Day'
          },
          {
            'ship_cost' => '13.63',
            'ServiceType' => 'FEDEX_EXPRESS_SAVER',
            'ship_note' => '3 Business Days Delivery by 4:30 pm',
            'ship_tag' => 'Fedex Express Saver'
          },
          {
            'ship_cost' => '7.75',
            'ServiceType' => 'FEDEX_GROUND',
            'ship_note' => '1-5 Business Days Delivery day based on di
+stance to destination',
            'ship_tag' => 'Fedex Ground'
          }
        ];
        
for (@{ $rtn }) {
    if ($_->{ServiceType} eq 'FEDEX_2_DAY') {
        print "$_->{ship_cost}\n";
    }
}

__END__

17.5
[download]

• perldsc
• Writeup Formatting Tips

the answers are in perldoc perldsc and perldoc perllol

Assuming your array is called @array, this might do it:

for my $i ( 0 .. $#array ) {
    next unless $array[$i]->{ServiceType} eq 'FEDEX_2_DAY';
    print $array[$i]->{ship_cost} and last;
}
[download]

Cheers, Sören