= Solution
The <antiquark> $\bar d$ in the specified $\overline B_d^0=b\bar d$ is a spectator. For the charmed final state the leading external-<W boson> tree is
$$
b\to c+W^-,\qquad W^-\to d+\bar u,
$$
with $c\bar d=D^+$ and $d\bar u=\pi^-$. For the charmless final state replace the active transition by $b\to u+W^-$, giving $u\bar d=\pi^+$ and the same $d\bar u=\pi^-$. Their weak amplitudes have factors $V_{cb}V_{ud}^*$ and $V_{ub}V_{ud}^*$, respectively, up to an irrelevant overall conjugation convention.
\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2021-b-decay-diagrams.png]
{title=Leading spectator diagrams for the charmed and charmless neutral-B decays}
The diagrams determine the leading weak flavour factors. Strong-interaction matrix elements and, particularly for the charmless channel, additional <loop diagrams> can also contribute to physical <branching fractions>.
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