Making the table enumerated

The paralist package allows this. For your example:

\documentclass{article}
\usepackage{paralist}

\begin{document}

\begin{enumerate}

\item Solve these equations:

\begin{inparaenum}
\item eq 1 \item eq 2 \item eq 3\\
\item eq 4 \item eq 5 \item eq 6
\end{inparaenum}

\end{enumerate}

\end{document}

You will probably want to insert some horizontal spacing after the content of each of the items.

If you don't need the equations aligned then you should us enumerate* from the enumitem package, which produces results similar to inparaenum, but provides more flexibility.

However, if you want them aligned, the array (since it is entirely math content) environment, or tabular is the solution to use:

Notes:

• I have used a \newcolumntype from the array package to simplify the use of the array or tabular environments in adding the labels.
• Also see What are the differences between using paralist vs. enumitem

Code:

\documentclass{article}

\usepackage[inline]{enumitem}% {enumerate*}
\usepackage{array}%            \newcolumntype

\newcounter{Label}
\newcommand*{\AddLabel}{\stepcounter{Label}(\alph{Label})~}%
\newcolumntype{R}{>{\AddLabel}l<{}}

\begin{document}
\begin{enumerate}

\item Solve these equations (enumerate*):

\noindent
\begin{enumerate*}
\item $x+3=7$ \item $x^2+5x-7=0$ \item $3x^4+5x^2-6x+7=0$
\item $az^2+bx+c=0$ \item $\sin x +\cos x =0$ \item $\cos x =-1$
\end{enumerate*}

\item Solve these equations (array):

\noindent
$\begin{array}{RRR}
 x+3=7       & x^2+5x-7=0        & 3x^4+5x^2-6x+7=0 \\
 az^2+bx+c=0 & \sin x +\cos x =0 & \cos x =1
\end{array}$

\end{enumerate}
\end{document}