The limit of the given expression $\lim_{{x \to 2}} \frac{{x^2 + 2x - 8}}{{2x^2 - 7x + 6}}$ is $6$.

Would you like any further details on the solution? Here are 5 related questions you might find interesting:

1. How do you factor the numerator and denominator of the expression?
2. What happens if the denominator were to be zero at $x = 2$?
3. Can this limit be solved using L'Hopital's Rule?
4. How would you handle a similar limit where the function is not rational?
5. How can limits be used in real-world applications, like physics or engineering?

Tip: Always check for indeterminate forms like $\frac{0}{0}$ before applying L'Hopital's Rule in limits.