STRATEGY: Upon reading any GRE Multiple Choice question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily plug in values of x to test for equivalency.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also apply some algebraic factoring techniques to simplify the given expression.
Since I feel both techniques are equally fast, I'm going to test for equivalency since I'm less likely to make mistakes with that technique.

Key concept: If two expressions are equivalent, they must evaluate to the same value for every possible value of x.
For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x.
So, if x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35, and the expression 5x = 5(7) = 35

Let's evaluate the given expression for \(x = 0\).

We get: \(\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}=\frac{2(0)^2(0 + 3) -2(0) -6}{(0)^2 + 2(0) - 3}=\frac{-6}{-3} = 2\)

We'll now evaluate each answer choice for \(x = 0\) and eliminate those that don't evaluate to \(2\)
(A) \(2(0)^2 - 2 = -2\). Doesn't evaluate to \(2\). ELIMINATE.
(B) \(2(0) + 2 = 2\). KEEP
(C) \(0 + 1 =1\). Doesn't evaluate to \(2\). ELIMINATE.
(D) \(2(0) + 6 = 6\). Doesn't evaluate to \(2\). ELIMINATE.
(E) \(0 - 1 = -1\). Doesn't evaluate to \(2\). ELIMINATE.

Answer: B