As given that $|\vec{A}|=2$ and $|\vec{B}|=4$
(a)
$$
\begin{aligned}
&\vec{A} \vec{B}=|\vec{A}||\vec{B}| \cos \theta=0 \\
&\Rightarrow 2 \times 4 \cos \theta=0 \\
&\Rightarrow \cos \theta=0 \Rightarrow \cos \theta=\cos 90^{\circ}
\end{aligned}
$$
Hence $\theta=90^{\circ}$
$\therefore$ Option (a) matches with option (ii).
(b)
$$
\begin{aligned}
&\vec{A} \vec{B}=|\vec{A} \| \vec{B}| \cos \theta=8 \\
&\Rightarrow 2 \times 4 \cos \theta=8 \\
&\Rightarrow \cos \theta=1 \Rightarrow \cos \theta=\cos 0^{\circ}
\end{aligned}
$$
Hence $\theta=0^{\circ}$
$\therefore$ Option (b) matches with option (i).
(c)
$$
\begin{aligned}
&\vec{A} \vec{B}=|\vec{A} \| \vec{B}| \cos \theta=4 \\
&\Rightarrow 2 \times 4 \cos \theta=4 \\
&\Rightarrow \cos \theta=\frac{1}{2} \Rightarrow \cos \theta=\cos 60^{\circ} \\
&\text { Hence } \theta=60^{\circ}
\end{aligned}
$$
$\therefore$ Option (c) matches with option (iv).
(d)
$$
\begin{aligned}
&\vec{A} \vec{B}=|\vec{A}||\vec{B}| \cos 0=-8 \\
&\Rightarrow 2 \times 4 \cos \theta=-8 \\
&\Rightarrow \cos \theta=-1 \Rightarrow \cos \theta=180^{\circ} \\
&\text { Hence, } \theta=180^{\circ} .
\end{aligned}
$$
$\therefore$ Option (d) matches with option (iii).