Indeed, \centering is the declaration, while \center is the environment. LaTeX is somewhat forgiving about this, but I don't think tex4ht can be. Sorry. Closing ...

1. With following source code of latex(say abc.tex):

\documentclass{article}
\begin{document}
\section {Preface}
\section {Preparation}
\subsection {Part A}
\begin{enumerate}
\item {Item 1}
\item {
Item 2

{\center This is a centered text}
Something about 2
}

\end{enumerate}

\subsection {Part B}
Part b goes here
\end{document}

2. generate abc.html with command `htlatex abc.tex`

3. check abc.html