I notice that this is a quadratic function with a negative coefficient for the $x^2$ term, so it will have a downward parabola shape. That means the maximum value will occur at the vertex of the parabola, which is the point where the slope of the function changes from positive to negative. To find the vertex, I can use the formula $x = -b/2a$, where $a$ and $b$ are the coefficients of the $x^2$ and $x$ terms respectively. In this case, $a = -1$ and $b = -6$, so plugging them into the formula, I get $x = -(-6)/2(-1) = 6/-2 = -3$. This is the value of $x$ that will give the maximum value for the function. 
What value of $x$ will give the maximum value for $-x^2- 6x + 12$?