First of all the following doesn't make sense. sub is called with the same parameters every time.

foreach (@temp)
   {
      sub($x0, $y0, $x1, $y1, @temp)
   }
}
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But lets see if I understand your problem. It seems you have an unnecessary loop there. I commented that out. Also I changed your inner loops slightly, they have to stop looping after they get to the last 4 values.

Now all there is left to do is to take your best attempt and wrap the corrected code for the other hash around it, substituting $x2...$y3 with @temp. I put the inner loop into a sub, makes it easier to compare to your version

foreach my $key (keys %other_hash)
    {
#    foreach (@{$other_hash{$key}}
#        {
        for (my $i=0; $i<=@{$points_by_name{$key}}-4; $i+=2)
            {
            innerloop( @{$other_hash{$key}}[$i..$i+3] );
            }
#        }
    }
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and

sub innerloop {
    my ($x2,$y2,$x3,$y3)= @_;
    foreach my $key (keys %points_by_name)
        {
#        foreach (@{$points_by_name{$key}}
#            {
            for (my $i=0; $i<=@{$points_by_name{$key}}-4; $i+=2)
                {
                sub(@{$points_by_name{$key}}[$i..$i+3], $x2, $y2, $x3,
+ $y3)
                }
#            }
        }
    }
[download]

Note I didn't test this. Might still be some bug in it.

About your 'keeping track' problem: You have $key, you have $i, what else do you need to know about the line you are evaluating? Pass them into the sub if the sub needs to know