= Solution
The species that oxidizes <nickel> is \b[<gold>(III) <ion>], rather than metallic <gold>. The <half-reactions> are
$$
\begin{aligned}
\mathrm{Ni}&\longrightarrow\mathrm{Ni^{2+}}+2e^-,\\
\mathrm{Au^{3+}}+3e^-&\longrightarrow\mathrm{Au}.
\end{aligned}
$$
Multiplying the first by three and the second by two gives
$$
\boxed{\mathrm{3Ni+2Au^{3+}\longrightarrow3Ni^{2+}+2Au}}.
$$
Standard <electrode potentials> are not multiplied by the balancing factors. Thus $E^\circ_{\rm cell}=1.50-(-0.25)=1.75\,\mathrm V$ and six <moles> of <electrons> are transferred per <mole> of this balanced reaction:
$$
\boxed{\Delta G^\circ=-6FE^\circ_{\rm cell}\simeq-1.01\times10^6\,\mathrm{J\,mol^{-1}}}.
$$
The negative sign predicts a thermodynamically favorable <galvanic replacement> under standard conditions.
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