The function provided in the image is:

$f(x) = \frac{x^2 + 2}{x^2 + 4x + 4}$

To find the x-intercepts, we need to solve for when the numerator equals zero. That is, we solve the equation:

$x^2 + 2 = 0$

Let's proceed with this:

$x^2 = -2$

This equation has no real solutions because the square of any real number is non-negative, and $-2$ is negative. Therefore, there are no real x-intercepts.

The correct answer is:

$\boxed{\text{None}}$

Would you like more details or further explanation? Here are some questions to expand your understanding:

1. What are x-intercepts, and how do they relate to the function's graph?
2. How do we interpret complex solutions if they arise in other situations?
3. What is the denominator's role when identifying intercepts?
4. How would this change if the numerator had real roots?
5. Can you visualize how this function behaves on a graph?

Tip: To find x-intercepts, always check when the numerator of a rational function equals zero, as long as the denominator does not also equal zero at the same points.