This is a solution based on the shortlst package, with a small patch: I introduced $3$ keys: nc (number of columns; $3$ by default), il (interline stretch, 1 by default, may be useful in case of very high formulae) and ls (the value of \labelsep, 0.6em by default). It also uses xkeyval and setspace.
An \item, if larger than one column, will occupy as many columns as necessary. I introduce a \paritem command, that sets the item body in a \parbox that occupies a chosen number of columns (1 by default). It gives a way to control the number of columns that an item occupies.
\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[showframe, nomarginpar]{geometry}
\usepackage{shortlst,setspace,xkeyval}%
\makeatletter
\newcounter{ncol}
\define@key{lex}{nc}[3]{\setcounter{ncol}{#1}}%% 3 columns by default
\define@key{lex}{il}[1.5]{\def\@intln{#1}}% interlining![1]
\define@key{lex}{ls}[0.6em]{\setlength{\labelsep}{#1}}%%distance between label and item body
\newenvironment{tabenumerate}[1][]{%\setlength\labelsep{0.6em}
\setkeys{lex}{nc,il,ls, #1}
\settowidth{\labelwidth}{\mbox{\itshape Problem 0\hskip0.25em}}
\setlength{\leftmargini}{\dimexpr\labelwidth+\labelsep\relax}%[1][3]
\setlength{\shortitemwidth}{\dimexpr\linewidth/\value{ncol}-\labelwidth-2\labelsep\relax}%
\setstretch{\@intln}
\everymath{\displaystyle}
\begin{shortenumerate}}%
{\end{shortenumerate}
}%
\newcommand\paritem[2][1]{\item \parbox[t]{\dimexpr#1\shortitemwidth +(\labelwidth + \labelsep + \itemindent)* \numexpr#1-1\relax\relax}{\setstretch{1}\leavevmode#2\strut\medskip}}
\makeatother
\renewcommand{\labelenumi}{\itshape Problem \arabic{enumi}.}
\makeatother
\begin{document}
\noindent Solve the following equations:
\begin{tabenumerate}[nc=3]
\item Stuff here.
\item Next thing’s stuff here. It requires 2 columns. \label{pb2}
\item Stuff there.
\paritem{Equation $4$ is another long equation in only one column. }
\item Still stuff.
\paritem[2] {\label{pb6} Equation $6$ is a second long equation. It stretches along two columns and no more.}
\item A small problem.
\item Equation $8$ is also a very very long equation, but its stretches ‘naturally’.
\end{tabenumerate}
We see by problems \ref{pb2} and \ref{pb6} that cross-references seem to work in this context.
\end{document} %
