To independently practice solving basic absolute value equations, evaluate the given statements $|x| = 2$, $|y| = -4$, and $|z| = 0$ using absolute value properties. For the equation $|x| = 2$, applying the property results in the equivalent equations $x = -2$ or $x = 2$, providing a two-part solution. For the equation $|y| = -4$, since the distance represented by an absolute value can never logically be negative, there is immediately no possible solution. Lastly, for the equation $|z| = 0$, the only valid equivalent equation is $z = 0$, resulting in a single definitive solution.