Write both sides in fractional form and cross multiply.
$$ \frac{12}{z}=60$$
$$ \frac{12}{z}\xcancel{=}\frac{60}{1}$$
$$ 60(z)=12(1) \tag*{\tiny divide by 60 on both sides}$$
$$ z=\frac{12}{60} \tag*{\tiny simplify} $$
$$ \boxed{z=\frac{1}{5}} $$
Take the reciprocal of both sides. This is basically a shortcut that uses the method shown in approach 1.
$$ \frac{12}{z}=60$$
$$ \frac{z}{12}=\frac{1}{60} \tag*{\tiny multiply both sides by 12}$$
$$ \boxed{z=\frac{1}{5}}$$