You can use for example leftmargin =3cm,
to get what you want.
See the complete code
\documentclass{article}
\usepackage{enumitem}
\begin{document}
\begin{description}[%
labelindent=1em,
labelwidth=1.2cm,
labelsep*=1em,
leftmargin =3cm, % <==================================================
itemindent= 0pt,
style = sameline
]
\item[Input:] $a_1,\ldots,a_m$
\item[Output:] Can we do some operation on the given input to get some outcome using this methodology and using $a_1,\ldots,a_m$?
\end{description}
\end{document}
and the result:

To get the minimal shift to right you can use the following code (use the longest word Output:
to get the needed length):
\begin{description}[%
widest=Output:, % <===================================================
itemindent=*,
leftmargin=* % <======================================================
]
\item[Input:] $a_1,\ldots,a_m$
\item[Output:] Can we do some operation on the given input to get some outcome using this methodology and using $a_1,\ldots,a_m$?
\end{description}
So the following complete code
\documentclass{article}
\usepackage{enumitem}
\begin{document}
\begin{description}[%
labelindent=1em,
labelwidth=1.2cm,
labelsep*=1em,
leftmargin =3cm, % <==================================================
itemindent= 0pt,
style = sameline
]
\item[Input:] $a_1,\ldots,a_m$
\item[Output:] Can we do some operation on the given input to get some outcome using this methodology and using $a_1,\ldots,a_m$?
\end{description}
\begin{description}[%
widest=Output:, % <===================================================
itemindent=*,
leftmargin=* % <======================================================
]
\item[Input:] $a_1,\ldots,a_m$
\item[Output:] Can we do some operation on the given input to get some outcome using this methodology and using $a_1,\ldots,a_m$?
\end{description}
\end{document}
shows both solutions and there difference:
