Several things there that can be improved on. ;)

The first is that $ref is a hash reference. More likely you simply want a hash:

my %ref;
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Perl allows some syntactic sugar that removes all those -> so you can write:

$ref{car}{Toyota}[2]="Corolla";
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However if you want to initialize a hash then you can:

my %ref = (
    car => {
        Honda => [qw(Civic Accord)],
        Toyota => [qw(Camry Tundra Corolla)],
        }
    );
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taking advantage of qw so that the car names don't require quoting.