We are asked to multiply and simplify the expression $(6 - \sqrt{5})(3 + \sqrt{5})$.

1. Problem Description

We are asked to multiply and simplify the expression $(6 - \sqrt{5})(3 + \sqrt{5})$.

2. Solution Steps

We can use the distributive property (also known as the FOIL method) to expand the expression.

$(a + b)(c + d) = ac + ad + bc + bd$

Applying this to our problem:

$(6 - \sqrt{5})(3 + \sqrt{5}) = 6(3) + 6(\sqrt{5}) - \sqrt{5}(3) - \sqrt{5}(\sqrt{5})$

Now, we can simplify each term:

$6(3) = 18$

$6(\sqrt{5}) = 6\sqrt{5}$

$-\sqrt{5}(3) = -3\sqrt{5}$

$-\sqrt{5}(\sqrt{5}) = -5$

So, we have:

$18 + 6\sqrt{5} - 3\sqrt{5} - 5$

Combine the constant terms and the terms with $\sqrt{5}$:

$(18 - 5) + (6\sqrt{5} - 3\sqrt{5}) = 13 + 3\sqrt{5}$

3. Final Answer

$13 + 3\sqrt{5}$