This example uses the tikzmark
library which was developed in response to questions asked on this site of the sort Peter Grill linked to in his answer:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{tikzmark,calc,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[remember picture, overlay]
\node (rightenum) at (.15\textwidth,0) {};
\draw [decorate, decoration={brace}, thick] ($({pic cs:top1} -| rightenum) + (0, 1em)$) -- ({pic cs:bot1} -| rightenum) node [midway, right] {first two items};
\draw [decorate, decoration={brace}, ultra thick] ($({pic cs:top2} -| rightenum) + (0, 1em)$) -- ({pic cs:bot2} -| rightenum) node [midway, right] {last four items};
\end{tikzpicture}
\begin{enumerate}
\item\tikzmark{top1} first
\item\tikzmark{bot1} second
\item\tikzmark{top2} third
\item fourth
\item fifth
\item\tikzmark{bot2} sixth
\end{enumerate}
\end{document}
\documentclass{...}
and ending with\end{document}
.tikzmark
which you can use to mark places in the enumeration and then use to position the curly brackets appropriately. There was a similar question earlier about doing this with a table and one of the comments mentioned this method.