Let's simplify the expression step-by-step:

$(x+6)(x+6) - 12x$

First, expand $(x+6)(x+6)$:

$(x+6)(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36$

Now, subtract $12x$:

$x^2 + 12x + 36 - 12x$

The $+12x$ and $-12x$ cancel each other out:

$x^2 + 36$

So, the simplified expression is:

$x^2 + 36$

Would you like further details or have any questions?

Here are some related questions to explore:

1. How do you expand binomials in general?
2. What is the difference between a perfect square and a difference of squares?
3. How can you factor the expression $x^2 + 36$?
4. What happens if you add or subtract other terms to this expression?
5. Can this be related to the Pythagorean Theorem?

Tip: Always double-check when simplifying expressions to ensure no terms are missed or incorrectly combined!