The equation you've provided is:
\[ \frac{14}{6}C \rightarrow \frac{14}{7}N + \frac{0}{-1}e \]
In this equation, a carbon-14 nucleus (with 6 protons) decays into a nitrogen-14 nucleus (with 7 protons) and emits a beta particle (an electron) represented by \(\frac{0}{-1}e\).
This type of decay involves the conversion of a neutron into a proton, which is characteristic of beta-minus decay. Therefore, the correct response is:
beta-minus decay.