#### Answer

{$4$}

#### Work Step by Step

Step 1: $\sqrt[3] {x-12}=-2$
Step 2: Raising each side of the equation to the power of $3$ and simplifying, we obtain:
$(\sqrt[3] {x-12})^{3}=(-2)^{3}$
$x-12=-8$
Step 3: Solving the equation, we obtain:
$x-12=-8$
$x=-8+12$
$x=4$
Therefore, the solution set of the equation is {$4$}.