C

Step 1: Identify the given vector components.
For vector C:
- $c_x = 5.0$ miles
- $c_y = 0$ miles
- $c_z = -2.0 imes d_z$ miles (we are initially unaware of $d_z$, so we'll determine it later).

For vector D:
- $d_x = -3.0$ miles
- $d_y = 4.0$ miles
- $d_z = 6.0$ miles.

Step 2: Calculate $c_z$ using the value of $d_z$.
- $c_z = -2.0 imes 6.0 = -12.0$ miles.

Now we have:
- For vector C: $c = (5.0, 0, -12.0)$
- For vector D: $d = (-3.0, 4.0, 6.0)$

Step 3: Find the resultant vector by summing components:
- Resultant $R_x = c_x + d_x = 5.0 + (-3.0) = 2.0$ miles
- Resultant $R_y = c_y + d_y = 0 + 4.0 = 4.0$ miles
- Resultant $R_z = c_z + d_z = -12.0 + 6.0 = -6.0$ miles

Step 4: The vector sum of displacements is therefore:
$R = (2.0, 4.0, -6.0)$ miles.

Step 5: The final answer, showcasing the vector displacement is:
C: (2.0, 4.0, -6.0).