To solve the quadratic equation \(x^2 - x - 2 = 0\), we can factorize the equation:

1. First, we look for two numbers that multiply to \(-2\) (the constant term) and add to \(-1\) (the coefficient of \(x\)).

The numbers are \(2\) and \(-1\).

2. So, we can factorize the equation as:
\[
(x - 2)(x + 1) = 0
\]

3. Now, set each factor equal to zero:
\[
x - 2 = 0 \quad \text{or} \quad x + 1 = 0
\]

Solving these gives:
\[
x = 2 \quad \text{or} \quad x = -1
\]

Thus, the solutions are \(x = 2\) and \(x = -1\).

The correct answer is C. x = -1 or 2.