The problem asks us to multiply and simplify the expression:

$(c + 6)(c - 6)$

This expression is a difference of squares. The formula for multiplying binomials of the form $(a + b)(a - b)$ is:

$(a + b)(a - b) = a^2 - b^2$

Here, $a = c$ and $b = 6$. Substituting these values into the formula:

$(c + 6)(c - 6) = c^2 - 6^2$

Simplify $6^2$:

$c^2 - 6^2 = c^2 - 36$

The simplified answer is:

$c^2 - 36$

Would you like additional details or have any questions? Here are some related questions to consider:

1. What is the difference of squares formula, and why does it work?
2. How do you recognize when an expression is a difference of squares?
3. Can this type of simplification be reversed, and how would you factor $c^2 - 36$?
4. How does this technique apply to solving quadratic equations?
5. What happens if the numbers in the binomials are not integers (e.g., $(c + x)(c - x)$)?

Tip: Always look for special patterns like the difference of squares when multiplying binomials—they simplify your work!