Geometry margin causing tasks alignment issue

One should reset \@rightskip. Imho the tasks package should do it. So make a bug report:

\documentclass[12pt]{article}

\usepackage{amsmath,geometry}
\usepackage{tasks}


\geometry{a4paper, margin=2cm}
\NewTasks[counter-format={tsk[a])}]{problems}[\item](4)

\begin{document}\raggedright

\begin{enumerate}
    \item Prove the following:
    \begingroup
    \makeatletter 
    \@rightskip=0pt
    \begin{problems}(4)
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \item $x$
        \end{problems}
      \endgroup         
    \end{enumerate}

\end{document}

Could a solution with \RaggedRight from ragged2e package be acceptable?

EDIT: Ulrike has already given the perfect answer but I'd like to add TeXnician's suggestion (\usepackage[none]{hyphenat}) to my original answer:

\documentclass[12pt]{article}

\usepackage[none]{hyphenat}

\usepackage{amsmath,geometry,tasks}
\geometry{a4paper, margin=2cm}
\NewTasks[counter-format={tsk[a])}]{problems}[\item](4)
\usepackage{ragged2e}

\usepackage{mwe}

\begin{document}\RaggedRight
    \blindtext
    \begin{enumerate}
        \item \blindtext Prove the following:
        \begin{problems}(4)
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
        \end{problems}
    \end{enumerate}
    \blindtext
\end{document}

Moreover, as egreg suggested to me in chat, another simple solution could be justifying only the problems environment:

\documentclass[12pt]{article}

\usepackage{amsmath,geometry,tasks}
\geometry{a4paper, margin=2cm}
\NewTasks[counter-format={tsk[a])}]{problems}[\item](4)
\usepackage{ragged2e}

\usepackage{mwe}

\begin{document}\raggedright
    \blindtext
    \begin{enumerate}
        \item \blindtext Prove the following:
        \begin{justify}
        \begin{problems}(4)
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
            \item $x$
        \end{problems}
        \end{justify}
    \end{enumerate}
    \blindtext
\end{document}

The output is more or less the same as before: