As given that $|\vec{A}|=2$ and $|\vec{B}|=4$
(a)
$$
\begin{aligned}
&|\vec{A} \times \vec{B}|=|\vec{A}||\vec{B}| \sin \theta=0 \\
&\Rightarrow 2 \times 4 \times \sin \theta=0 \\
&\Rightarrow \sin \theta=0 \Rightarrow \sin \theta=\sin 0^{\circ}
\end{aligned}
$$
Hence $\theta=0^{\circ}$.
$\therefore$ Option (a) matches with option (iv).
(b) $|\vec{A} \times \vec{B}|=|\vec{A} \| \vec{B}| \sin \theta=8$
$$
\begin{aligned}
&\Rightarrow 2 \times 4 \sin \theta=8 \\
&\Rightarrow \sin \theta=1=\sin 90^{\circ}
\end{aligned}
$$
Hence $\theta=90^{\circ}$
$\therefore$ Option (b) matches with option (iii).
$$
\text { (c) } \begin{aligned}
&|\vec{A} \times \vec{B}|=|\vec{A}||\vec{B}| \sin \theta=4 \\
&\Rightarrow 2 \times 4 \sin \theta=4 \\
&\Rightarrow \sin \theta=\frac{1}{2}=\sin 30^{\circ}
\end{aligned}
$$
Hence, $\theta=30^{\circ}$.
$\therefore$ Option (c) matches with option (i).
(d)
$$
\begin{aligned}
&|\dot{A} \times \dot{B}|=|\dot{A}||\dot{B}| \sin \theta=4 \sqrt{2} \\
&\Rightarrow 2 \times 4 \sin \theta=4 \sqrt{2} \\
&\Rightarrow \sin \theta=\frac{1}{\sqrt{2}}=\sin 45^{\circ}
\end{aligned}
$$
Hence, $\theta=45^{\circ}$.
$\therefore$ Option (d) matches with option (ii).