A couple of options, depending on what appeals to you:

my $num = keys %{ $hash{key} };

# or

my $ref = $hash{key}; my $num = keys %$ref;
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The first one is short-hand for accessing the second-level hash directly, though I find it a tad ugly, especially if the structures get deeper than two levels. The second one grabs the reference for the second level hash and then calls keys on that, which is a bit more explicit.