2

I'd like to know how to align the enumerate list nested inside the description by the vertical black line as shown in the picture.

\begin{document}

    \begin{description}\item[Description]
        \begin{enumerate}[leftmargin=4cm]
            \item Item
            \item Another item
            \item Last item
        \end{enumerate}
    \end{description}

\end{document}

enter image description here

2

You want to set 4cm as the \leftmargin for description (with a correction for the \labelsep).

\documentclass{article}
\usepackage{enumitem}

\usepackage{showframe} % just to show the margins of the text block

\begin{document}

\begin{description}[leftmargin=4cm,labelwidth=\dimexpr4cm-\labelsep]

\item[Description]
  \begin{enumerate}[leftmargin=*]
  \item Item
  \item Another item
  \item Last item
  \end{enumerate}

\end{description}

\end{document}

enter image description here

2

If you want to have the minimal distance between the description items and the enumerate items, you can obtain it eaasily with calc and enumitem:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{calc}
\usepackage{enumitem}

\begin{document}

    \begin{description}[leftmargin=\widthof{\textbf{Description}} + \labelsep , style = unboxed]\item[Description]
        \begin{enumerate}[wide=0pt, leftmargin =*]
            \item Item
            \item Another item. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text
            \item Last item
        \end{enumerate}
    \end{description}

\end{document} 

enter image description here

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