How to put 6 images in 3 columns-2 rows?

One more suggestion:

• make figure content centered with use of \centering
• between sub figures insert \hfil
• purpose of \quad is not clear, let remove it
• centering of subfigure content is surplus. Rather make sub figure width smaller and adopt figure width to width of subfigure

Complete code:

\documentclass{article}
\usepackage{graphicx} 
\usepackage{caption,subcaption}
\usepackage[showframe]{geometry}

\begin{document}
\begin{figure}[htb]
    \centering % <-- added
\begin{subfigure}{0.25\textwidth}
  \includegraphics[width=\linewidth]{example-image-a}
  \caption{image1}
  \label{fig:1}
\end{subfigure}\hfil % <-- added
\begin{subfigure}{0.25\textwidth}
  \includegraphics[width=\linewidth]{example-image-b}
  \caption{image2}
  \label{fig:2}
\end{subfigure}\hfil % <-- added
\begin{subfigure}{0.25\textwidth}
  \includegraphics[width=\linewidth]{example-image-c}
  \caption{image3}
  \label{fig:3}
\end{subfigure}

\medskip
\begin{subfigure}{0.25\textwidth}
  \includegraphics[width=\linewidth]{example-image-a}
  \caption{image4}
  \label{fig:4}
\end{subfigure}\hfil % <-- added
\begin{subfigure}{0.25\textwidth}
  \includegraphics[width=\linewidth]{example-image-b}
  \caption{image5}
  \label{fig:5}
\end{subfigure}\hfil % <-- added
\begin{subfigure}{0.25\textwidth}
  \includegraphics[width=\linewidth]{example-image-c}
  \caption{image6}
  \label{fig:6}
\end{subfigure}
\caption{Fasi del processo di impregnazione}
\label{fig:images}
\end{figure}
\end{document}

The result is:

I don't think you need those \quads. Add a blank line between the rows.

\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{caption, subcaption}
\usepackage[showframe]{geometry}

\begin{document}

\begin{figure}[H]
  \begin{subfigure}{0.3\textwidth}
    \centering
    \includegraphics[width=.8\linewidth]{imp₁.png}
    \caption{image1}
    \label{fig:1}
  \end{subfigure}%
  \begin{subfigure}{0.3\textwidth}
    \centering
    \includegraphics[width=.8\linewidth]{imp₂.png}
    \caption{image2}
    \label{fig:2}
  \end{subfigure}
  \begin{subfigure}{0.3\textwidth}\quad
    \centering
    \includegraphics[width=.8\linewidth]{imp₃.png}
    \caption{image3}
    \label{fig:3}
  \end{subfigure}
  \medskip

  \begin{subfigure}{0.3\textwidth}
    \centering
    \includegraphics[width=.8\linewidth]{imp₄.png}
    \caption{image4}
    \label{fig:4}
  \end{subfigure}
  \begin{subfigure}{0.3\textwidth}
    \centering
    \includegraphics[width=.8\linewidth]{imp₅.png}
    \caption{image5}
    \label{fig:5}
  \end{subfigure}
  \begin{subfigure}{0.3\textwidth}
    \centering
    \includegraphics[width=.8\linewidth]{imp₆.png}
    \caption{image6}
    \label{fig:6}
  \end{subfigure}
  \caption{Fasi del processo di impregnazione}
  \label{fig:images}
\end{figure}

\end{document} 

You did \quad before the the third \includegraphics moving it behind it like in the other cases should fix it.

\begin{figure}[H]
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=.8\linewidth]{imp_1.png}\quad
  \caption{image1}
  \label{fig:1}
\end{subfigure}%
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=.8\linewidth]{imp_2.png}\quad
  \caption{image2}
  \label{fig:2}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}%"\quad" not here since this will insert a spacing before the image.
  \centering
  \includegraphics[width=.8\linewidth]{imp_3.png}\quad %but here
  \caption{image3}
  \label{fig:3}
\end{subfigure}
\medskip
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=.8\linewidth]{imp_4.png}\quad
  \caption{image4}
  \label{fig:4}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=.8\linewidth]{imp_5.png}\quad
  \caption{image5}
  \label{fig:5}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=.8\linewidth]{imp_6.png}
  \caption{image6}
  \label{fig:6}
\end{subfigure}
\caption{Fasi del processo di impregnazione}
\label{fig:images}
\end{figure}