You have two options:

1. Change your data structure to an array of hashes.
2. Sort the indices, then apply the sorted indices as a slice to each array.

The first option is better because you end up with a better data structure.

my @values = (
    { name => 'fred', index => 2 },
    { name => 'bob', index => 1 },
    { name => 'john', index => 4 },
    { name => 'peter', index => 3 },
);

my @sorted_values = sort { $a->{index} <=> $b->{index} } @values;
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If you wanted to take option 2 because, for instance, you cannot change the data structures in question, you could do something like:

my @sorted_indices = sort { $array_b[$a] <=> $array_b[$b] } 0 .. $#arr
+ay_b;

@array_a = @array_a[@sorted_indices];
@array_b = @array_b[@sorted_indices];
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That, however, is much more fragile and depends a lot on you maintaining parallel data structures. The first option is much more robust and tolerant of change.