= Solution
The intersection with a line $\ell$ is a <hyperplane section>:
$$
D=\ell\cap C,\qquad \mathcal O_C(D)\cong\mathcal O_C(1).
$$
The <canonical bundle of a smooth projective hypersurface> formula, obtained from the <adjunction formula>, gives for a smooth degree-four curve in $\mathbb P^2$
$$
K_C\cong
\left(K_{\mathbb P^2}\otimes\mathcal O_{\mathbb P^2}(4)\right)|_C
\cong\mathcal O_C(-3+4)
\cong\mathcal O_C(1).
$$
\b[Thus $\mathcal O_C(D)\cong K_C$, so the <divisor class> of $D$ is the <canonical divisor> class. Therefore $D$ is a canonical divisor. Its degree is also $4=2g-2$, consistently with $g=3$.]
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