In a galvanic cell, the cathode is where reduction occurs, meaning that it is the site where electrons are gained.
In the given reaction:
Oxidation half-reaction (at the anode): \[ 2Cr(s) \rightarrow 2Cr^{3+}(aq) + 6e^- \]
Reduction half-reaction (at the cathode): \[ 3Cu^{2+}(aq) + 6e^- \rightarrow 3Cu(s) \]
Thus, the half-reaction that occurs at the cathode is:
\[ 3Cu^{2+}(aq) + 6e^- \rightarrow 3Cu(s) \]
This indicates that copper ions (\(Cu^{2+}\)) are being reduced to solid copper (\(Cu\)).