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.

You seem to have an extra level, a hash with a single key.

$ref->{Honda}->[0]="Civic";
$ref->{Honda}->[1]="Accord";
$ref->{Toyota}->[0]="Camry";
$ref->{Toyota}->[1]="Tundra";
$ref->{Toyota}->[2]="Corolla";
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By the way, the arrow between indexes can be omitted.

$ref->{Honda}[0]="Civic";
$ref->{Honda}[1]="Accord";
$ref->{Toyota}[0]="Camry";
$ref->{Toyota}[1]="Tundra";
$ref->{Toyota}[2]="Corolla";
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It seems odd to refer to array indexes using a constant.

$ref->{Honda}  = [ qw( Civic Accord         ) ];
$ref->{Toyota} = [ qw( Camry Tundra Corolla ) ];
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Or if you were in a loop,

push @{$ref->{Honda}}, 'Civic';
push @{$ref->{Honda}}, 'Accord';
push @{$ref->{Toyota}}, 'Camry';
push @{$ref->{Toyota}}, 'Tundra';
push @{$ref->{Toyota}}, 'Corolla';
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