Can't believe this hasn't been pointed out yet, but @array = {"a", "b", "c", "d"} leaves @array with one element, that element being a hashref. You want parentheses instead of braces.

Instead of the grep solution offered above, you can use List::Util's first.

#!/usr/bin/perl -l

use List::Util "first";

my @array = qw(a b c d);

my $index = first { $array[$_] eq "c" } 0..$#array;

die "c was not found in \@array" if ! defined $index;
print $array[$index-1];
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