The worst case time complexity of Mergesort is $k \times n \log n$ for an input of size $n$.
For an input of size $64$, the algorithm takes $30s$. Therefore,
$$\begin{align}
k \times 64 \log_2{64} &= 30s\\[1em]
k \times 384 &= 30s\\[1em]
\implies k &= 0.078125s
\end{align}$$
Let the size of the problem that can be solved in $6$ minutes be $x$. Then,
$$k \times x \log_2 x = 360s$$
From this, we get:
$$\begin{align}
x \log_2 x &= \frac{360s}{0.078125s}\\[1em]
\implies x &= 512
\end{align}$$
Correct Answer: $B$