We are given the equation:

$\log_4(x - 3) + \log_4(x + 3) = 2$

To solve for $x$, follow these steps:

Step 1: Apply the logarithmic property

Use the property of logarithms that states:

$\log_b(A) + \log_b(B) = \log_b(A \cdot B)$

This allows us to combine the two logarithms on the left-hand side:

$\log_4\left((x - 3)(x + 3)\right) = 2$

Step 2: Simplify the expression inside the logarithm

Notice that $(x - 3)(x + 3)$ is a difference of squares:

$(x - 3)(x + 3) = x^2 - 9$

Thus, the equation becomes:

$\log_4(x^2 - 9) = 2$

Step 3: Rewrite the equation in exponential form

Recall that $\log_b(A) = C$ is equivalent to $b^C = A$. Applying this property, we convert the logarithmic equation to an exponential