Your problem is that $i is only changed if $answer eq $numbers[$i]. You need to increment $i all the time. Or better, use a hash:

#usr/bin/perl
use strict;
use warnings;

my %numbers = qw(
    0 zero
    1 one
    2 two
    3 three
    4 four
    5 five
    6 six
    7 seven
    8 eight
    9 nine
    );

print "Enter a number\n";
chomp( my $input = <STDIN> );
print $numbers{ $input } if exists $numbers{ $input };
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