The expression given in the image is:

$\lim_{x \to 2} \frac{x^2 + 5x + 6}{x^2 + 4x}$

Let's break it down:

1. Substitute $x = 2$ into the expression:

   $\frac{2^2 + 5(2) + 6}{2^2 + 4(2)} = \frac{4 + 10 + 6}{4 + 8} = \frac{20}{12} = \frac{5}{3}$

So, the limit is:

$\boxed{\frac{5}{3}}$

Would you like further details or have any questions about this solution?

Here are 5 related questions for further practice:

1. What is the limit of $\lim_{x \to 3} \frac{x^2 + 2x + 1}{x^2 + 3x + 2}$?
2. How do you handle limits that result in an indeterminate form like $\frac{0}{0}$?
3. Can you find the limit of a function as $x \to \infty$ for rational expressions?
4. What is L'Hopital's Rule and when is it applied in limit problems?
5. How do you factor quadratic expressions to simplify limit problems?

Tip: Always check if direct substitution works first when solving limits. If it results in an indeterminate form, try factoring, canceling, or using other techniques like L'Hopital's Rule.