= Solution
Plot <position> $x$ horizontally and $ct$ vertically, with equal length scales, so vacuum light rays have slopes $\pm1$. A possible cause of the <spacetime event> $A$ must lie on or inside its <past light cone>, with $\Delta t=t_A-t_{\mathrm{cause}}>0$. Equivalently, <causality> requires $|\Delta x|\leq c\Delta t$.
From $B$ to $A$, $\Delta x=6\,\mathrm m$ and $\Delta t=10^{-8}\,\mathrm s$. Using $c\simeq3.00\times10^8\,\mathrm{m\,s^{-1}}$, the available light-travel distance is only $c\Delta t=3.00\,\mathrm m$. In the $(-,+,+,+)$ <metric signature>, the <Minkowski interval> is
$$
s_{BA}^2=(\Delta x)^2-c^2(\Delta t)^2\simeq36-9=27\,\mathrm{m^2}>0.
$$
There is <spacelike separation>, so a signal would need <speed> $6\times10^8\,\mathrm{m\,s^{-1}}\simeq2c$:
$$
\boxed{B\text{ cannot cause }A.}
$$
From $C$ to $A$, $\Delta x=-2\,\mathrm m$ and $\Delta t=1.5\times10^{-8}\,\mathrm s$. Now $c\Delta t=4.50\,\mathrm m>|\Delta x|$, giving
$$
s_{CA}^2\simeq4-20.25=-16.25\,\mathrm{m^2}<0.
$$
This is <timelike separation>, with a possible signal <velocity> $-2/(1.5\times10^{-8})\simeq-1.33\times10^8\,\mathrm{m\,s^{-1}}$. Therefore
$$
\boxed{C\text{ could cause }A,\text{ though the coordinates alone do not prove that it did.}}
$$
\Image[/past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2015-resit-causal-light-cone.png]
{title=The past light cone of event A contains C but excludes B}
{description=Original <spacetime diagram> using $ct$ in metres and $c\simeq3.00\times10^8\,\mathrm{m\,s^{-1}}$. The dashed B-to-A segment would require a superluminal signal; the C-to-A segment has a physically allowed subluminal slope.}
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