= Solution
Take any limiting cone $\ell_i:L\to D(i)$ in $\mathcal C$ of the given shape. Since $GF$ preserves such <categorical limits>, the cone $GF\ell_i:GFL\to GFD(i)$ is limiting in $\mathcal E$. It is the image under $G$ of the cone $F\ell_i$ in $\mathcal D$. Reflection by $G$ therefore says that $F\ell_i$ is limiting in $\mathcal D$. Since this works for every diagram and every limiting cone of the specified shape, \b[$F$ preserves <categorical limits> of that shape].
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