Natural join automatically equates every same-named attribute appearing in its two inputs.
The intended relationship is:
$\mathrm{Authors.au\_id=TitleAuthors.au\_id}$
then
$\mathrm{TitleAuthors.title\_id=Titles.title\_id}$
then
$\mathrm{Titles.pub\_id=Publishers.pub\_id}$.
However, the full $\mathrm{Authors}$ relation also contains
$\mathrm{address}$, $\mathrm{city}$, and $\mathrm{state}$.
$\mathrm{Publishers}$ contains these same attribute names.
If we carry all of these attributes through to the natural join with $\mathrm{Publishers}$, natural join may additionally require:
$\mathrm{Authors.address=Publishers.address}$
$\mathrm{Authors.city=Publishers.city}$
$\mathrm{Authors.state=Publishers.state}$.
Those conditions are not part of the query.
The fix is to project $\mathrm{Authors}$ down to only the attributes needed later:
$\pi_{\mathrm{au\_id,au\_fname}}(\mathrm{Authors})$.
Then the natural-join chain connects only through the intended identifiers.
Therefore, A is correct.