Answer:
The correct option is; 
C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
Please find attached the required function graph
Step-by-step explanation:
To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;
x  F(x)
       F(x)
-4 30
       30
-3 0
       0
-2 6
       6
-1 0
        0
0  -18
      -18
1 0
         0
2 150
       150
The shape of a graph with multiplicity of 2 
Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;
x = 1, -1, and, giving
(x - 1)·(x + 1)·(x - 3)² = 0 
Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.