The second argument is the distance between lines, so it should be larger. We also use \par-like argument called \endgraf. For example:

\documentclass[12pt,oneside]{book}
\begin{document} 

\begin{titlepage}
\begin{center}
\vspace*{0.1in}
\begingroup
%\fontsize{16pt}{12pt}\selectfont % PS
\fontsize{16pt}{20pt}\selectfont % PS
\textbf{A Solution Manual For}\\
\vspace*{0.5in}
%\fontsize{28pt}{22pt}\selectfont % PS
\fontsize{28pt}{34pt}\selectfont % PS
\textbf{Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.}
\endgraf
\endgroup
\end{center}
\end{titlepage}
\newpage\null\thispagestyle{empty}\newpage

This is the text

\end{document}

The second argument is the distance between lines, so it should be larger. We also use \par-like command called \endgraf. For example:

\documentclass[12pt,oneside]{book}
\begin{document} 

\begin{titlepage}
\begin{center}
\vspace*{0.1in}
\begingroup
%\fontsize{16pt}{12pt}\selectfont % PS
\fontsize{16pt}{20pt}\selectfont % PS
\textbf{A Solution Manual For}\\
\vspace*{0.5in}
%\fontsize{28pt}{22pt}\selectfont % PS
\fontsize{28pt}{34pt}\selectfont % PS
\textbf{Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.}
\endgraf
\endgroup
\end{center}
\end{titlepage}
\newpage\null\thispagestyle{empty}\newpage

This is the text

\end{document}