To solve this limit, we'll compute the derivative of the function at the given point using the definition of a derivative. The expression provided is:

$\lim_{{h \to 0}} \frac{{3(2 + h)^2 + 2 - 14}}{h}$

Let's go through the steps to solve this:

1. Expand the expression inside the limit:

   $3(2 + h)^2 + 2 - 14$

2. Simplify the numerator:

   $3(4 + 4h + h^2) + 2 - 14$

   $12 + 12h + 3h^2 + 2 - 14$

   $12 + 12h + 3h^2 - 12$

   $12h + 3h^2$

3. Factor out $h$ from the numerator:

   $\frac{{h(12 + 3h)}}{h}$

4. Cancel the $h$ in the numerator and the denominator:

   $\lim_{{h \to 0}} (12 + 3h)$

5. Take the limit as $h$ approaches 0:

   $12 + 3(0) = 12$

Thus, the derivative of the function at the given point is $\boxed{12}$.

Would you like a more detailed explanation of any of these steps?

Further Questions:

1. What is the definition of a derivative?
2. How do you find the derivative of a polynomial function?
3. Can you explain the power rule for differentiation?
4. How does the chain rule apply in differentiation?
5. What is the geometric interpretation of a derivative?
6. What are the common rules for finding derivatives?
7. Can derivatives be used to find the slope of a tangent line?
8. What are higher-order derivatives?

Tip: When taking the derivative, always simplify the expression as much as possible before applying limit laws.