When you did

my $d = ($n =~ /A/g)
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the global match (triggered by /g) was done at scalar context. In this case it finds a single match or fails. So $d will return 1 or 0.

To do what you want, you need to set a list context and then count the matches.

my $n = "ABCDABDIDAOFOOFAA" ;
my @matches = ($n =~ /A/g);
my $d = @matches;
print "matches $d";
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will output "matches 5".