To simplify the expression \((6 - 2i)(6 + 2i)\), we can use the fact that it represents a difference of squares:
\[ (a - b)(a + b) = a^2 - b^2 \]
Here, \(a = 6\) and \(b = 2i\). Therefore:
\[ (6 - 2i)(6 + 2i) = 6^2 - (2i)^2 \]
Calculating \(6^2\):
\[ 6^2 = 36 \]
Now, calculate \((2i)^2\):
\[ (2i)^2 = 4i^2 \]
Since \(i^2 = -1\), we have:
\[ 4i^2 = 4(-1) = -4 \]
Now, substituting back, we get:
\[ 36 - (-4) = 36 + 4 = 40 \]
So, the simplified expression is:
\[ \boxed{40} \]