Insert after={\hfill} in the description* options.
MWE
\documentclass{article}
\usepackage[inline,shortlabels]{enumitem}
\usepackage{tabto}
\begin{document}
\NumTabs{3}
\begin{description*}[before={\noindent},itemjoin={\tab},after={\hfill}]
\item {1.}
\item {2.}
\item {3.}
\item {4.}
\item {5.}
\item {6.}
\end{description*}
\end{document}
Output:

EDIT
To be able to do what you ask in the comment, we need to issue \hfill\par before the closing brace, otherwise the paragraph is not ended. For explanations see, for example, Incorrect line spacing when using \Large in a center environment.
This can be done with the help of the etoolbox package and the line
\AfterEndEnvironment{description*}{\hfill\par}
that adds \hfill\par after description* has ended.
MWE:
\documentclass{article}
\usepackage[inline,shortlabels]{enumitem}
\usepackage{tabto}
\usepackage{etoolbox}
\AfterEndEnvironment{description*}{\hfill\par}
\begin{document}
{\tiny\NumTabs{3}
\begin{description*}[before={\noindent},itemjoin={\tab},after={\hfill}]
\item {1.}
\item {2.}
\item {3.}
\item {4.}
\item {5.}
\item {6.}
\end{description*}}
\bigskip
\NumTabs{3}
\begin{description*}[before={\noindent},itemjoin={\tab},after={\hfill}]
\item {1.}
\item {2.}
\item {3.}
\item {4.}
\item {5.}
\item {6.}
\end{description*}
\bigskip
{\Huge\NumTabs{3}
\begin{description*}[before={\noindent},itemjoin={\tab},after={\hfill}]
\item {1.}
\item {2.}
\item {3.}
\item {4.}
\item {5.}
\item {6.}
\end{description*}}
\end{document}
Output:

taskspackage (part ofexsheets). My answer to How can I make two columns in two columns shows an example. – cgnieder Jan 12 '14 at 20:03