Cross-referencing enumerate item

Here is a different solution using the enumitem package. With it we can configure how references to items look. In this MWE I change the reference format of second level enumerate globally.

As an added bonus we do not have to mess with internals.

\documentclass[12pt]{article}
\usepackage{enumitem}
\setlist[enumerate,2]{
  ref=(\alph*),
}
\begin{document}

\begin{enumerate}
    \item Solve $x^2=1$.
    \item Solve $x^2=4$.
    \begin{enumerate}
        \item \label{enum:1} Find all roots.
        \item For each root in \ref{enum:1}, subtract 2 from it.
    \end{enumerate}
\end{enumerate}

\end{document}

The key is to redefine the macro \p@enumii, which holds the prefix used in this situation:

\documentclass[12pt]{article}
\begin{document}

\begin{enumerate}
    \item Solve $x^2=1$.
    \item Solve $x^2=4$.
    \begin{enumerate}
        \makeatletter
        \renewcommand*\p@enumii{}
        \makeatother
        \item \label{enum:1} Find all roots.
        \item For each root in (\ref{enum:1}), subtract 2 from it.
    \end{enumerate}
    \item To show that the redefinition is local:
    \begin{enumerate}
        \item \label{enum:2} Find all roots.
        \item For each root in (\ref{enum:2}), subtract 2 from it.
    \end{enumerate}
\end{enumerate}

\end{document}