The correct answer is $\boxed{\frac{1}{4}}$.
Marginal revenue is the additional revenue that a firm earns from selling an additional unit of output. It is calculated by taking the derivative of the total revenue function with respect to the quantity sold.
In this case, the demand curve is given by $p = 16 – \frac{1}{{sq}}$. The total revenue function is therefore $TR = pq = 16q – \frac{q^2}{4}$. The marginal revenue function is $MR = \frac{d}{dq}(TR) = 16 – \frac{q}{2}$.
At $q = 4$, the marginal revenue is $\frac{1}{4}$. This means that if the firm sells an additional unit of output, its revenue will increase by $\frac{1}{4}$.
The other options are incorrect because they do not correspond to the marginal revenue function. Option A, $16$, is the price of the first unit of output. Option B, $8$, is the average revenue when $q = 4$. Option C, $4$, is the marginal revenue when $q = 2$.