Explanation

To answer this question, it is important to understand what is meant by the phrase “directly proportional.”

It means that $a = kb$, where k is a constant.

In alternative form: = k, where k is a constant.

So, because they both equal the constant, $\frac{a_{old}}{b_{old}}=\frac{a_{new}}{b_{new}}$. Plugging in values: $\frac{8}{2}=\frac{a_{new}}{4}$.
Crossmultiply and solve:
$32 = 2a_{new}$
$a_{new} = 16$

We have two scenarios

$b^3 = a$ $(2^3 = 8)$

and

$4b = a$ $(4*2 = 8)$

Since the problem contains the words "directly proportional",

we must choose the second scenario and not the first. In other words, the graph should be a straight line and not an exponential curve.

So, if $b=4$, then the value of a must be $4*4 = 16$. Choice B

The exponential relationship will give us $4^3 = 64$, which is there as a trap answer.