To simplify the expression $(x - 6)^2$, we apply the square of a binomial formula:

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

In this case, $a = x$ and $b = 6$. Applying the formula:

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

So, the correct equivalent expression is:

$x^2 - 12x + 36$

This corresponds to option C.

Would you like more details on this expansion, or do you have other questions?

Here are some related questions:

1. What happens when you expand $(x + 6)^2$?
2. How do you factor a trinomial like $x^2 - 12x + 36$?
3. Can you explain the difference between $(x - 6)^2$ and $(x - 6)^3$?
4. What are some other examples of binomial expansions?
5. How does the distributive property apply to squaring binomials?

Tip: Always remember to apply the formula carefully when squaring binomials.