Once you expand the product, move the constant term to the other side so that you have $a^2$ alone on one side.

When you take the square root of both sides of an equation like $a^2 = \text{(expression)}$, you normally get two solutions, $a = \pm \sqrt{\text{(expression)}}$. How does the condition that $a$ is positive affect your choice?

In Desmos, type f(x) = (x + 4)(x - 4) to represent the left side as a function of $a$ (using $x$ as the variable).

Choose any positive number for $b$, for example $b = 5$. Then type the equation f(x) = 5. Desmos will show the $x$-values where $(x+4)(x-4) = 5$; these are the possible values of $a$ for that $b$.

For the same $b$ value (like $b=5$), type each expression from the choices into Desmos: b^2 + 16, b + 16, sqrt(b + 16), and 1/sqrt(b + 16) (with b replaced by your number, e.g. 5). The correct option is the one whose result matches the positive solution $x$ from the equation f(x) = b.

Use the difference of squares:

So the given equation becomes

Add $16$ to both sides of the equation:

To solve $a^2 = b + 16$ for $a$, take the square root of both sides:

Because the problem states that $a$ is positive, we must choose the positive square root only. Therefore,

which matches choice C.