you have to change the foreach in your inner loop for a while (right now it is only iterating once over the hash), or change the foreach inner loop to use keys %hash instead of each %hash (so it iterates over every key). Also, you are using == to compare the elements in the array to the keys in the hash, so this will only work for numeric values. You could try something like this instead:

foreach my $thing (@array) {
    if ( exists $hash {$thing} ) {
        push @new_array, $hash {$thing};
    }
}
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hope this helps,