C

Step 1: Let's denote the resistance of each equal resistor as R.
Step 2: When four resistors are connected in series, the equivalent resistance (S) is calculated as:
$S = R + R + R + R = 4R$.
Step 3: When the same four resistors are connected in parallel, the total resistance (P) is given by:
$$\frac{1}{P} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{4}{R}$$
Therefore,
$$P = \frac{R}{4}$$
Step 4: Given that S = nP, substituting the expressions for S and P:
$$4R = n \left(\frac{R}{4}\right)$$
Step 5: Cancelling R from both sides (assuming R is not zero):
$$4 = n \cdot \frac{1}{4}$$
Step 6: Solving for n:
$$n = 4 \times 4 = 16$$
Step 7: Hence, the minimum possible value of n is 16.
Therefore, the correct answer is option C.