Step 1: Definition of a transition element.
A transition metal must have an incomplete d-subshell either in the ground state or in any common oxidation state.
Step 2: Apply to Zn, Cd, Hg.
All three have completely filled d\(^{10}\) configuration in the ground state and in their stable +2 state. They never display a partially filled d-shell, so they are not transition metals.
\[ \boxed{Zn,\ Cd,\ Hg} \]