Enumeration inside a paragraph

You can load the enumitem package with the option inline. It defines the environment enumerate* which does exactly what you want.

If you also want to change the default numbering from 1. to (1.) you can also do that within enumitem. The following MWE does what you want.

\documentclass{article}

\usepackage[inline]{enumitem}

\begin{document}
    Note that
    \begin{enumerate*}[label=(\arabic*.)]
        \item  \label{1} this is an answer. 
        \item  By \ref{1}, we conclude that the answer works.
    \end{enumerate*}
\end{document}

You can use the enumitem package with the inline option. Starred enumerate environments will look like what you are asking for.

\documentclass{article}
\usepackage[inline]{enumitem}
\begin{document}
This is an example paragraph meant to demonstrate
\begin{enumerate}[label=(\arabic*)]
    \item how enumitem works
    \item with the inline option
    \item compared to the unstarred version
\end{enumerate}

This is an example paragraph meant to demonstrate
\begin{enumerate*}[label=(\arabic*)]
    \item how enumitem works
    \item with the inline option
    \item compared to the unstarred version
\end{enumerate*}
\end{document}