Instead of .*? you need to use something more complex, something that can handle quoted strings. Something like:

my $term = qr/"[^"\\]*(?>\\.[^"\\]*)*"|[^,"]*/;
[download]

(which can handle escaped (backslashed) contents, too, change to

my $term = qr/"[^"]*(?>""[^"]*)*"|[^,"]*/;
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if you escape quotes by doubling them)

And then you can do

/^$term,$term,$term,($term)/o;
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which seems to work well for me... BTW it's "while", not "While".

my $term = qr/"[^"\\]*(?>\\.[^"\\]*)*"|[^,"]*/;
while (<DATA>) {
  /^$term,$term,$term,($term)/o and print "$1\n";
}
__DATA__
6,0,3,"8.1",1
7,578,,"8.2,r1",1
8,0,5,"8.2,r3",1
18,0,13,"6.2",1
19,D610,,"6.3,r1",1
20,2f78,15,"6.3,r2",1
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Result:

"8.1"
"8.2,r1"
"8.2,r3"
"6.2"
"6.3,r1"
"6.3,r2"