The equation \( 146C \rightarrow 147N + 0^{-1}e \) represents beta-minus decay.
In this process, a neutron in the carbon-14 nucleus is transformed into a proton, and a beta particle (electron) is emitted. The notation \( 0^{-1}e \) indicates a beta particle (electron) being released, which is characteristic of beta-minus decay.
So, the correct response is:
beta-minus decay.