pgfmathparse basic usage

\pgfmathresult holds the result of the last computation done by pgfmath; in this case this was the evaluation of the y-coordinate of (4,-5), which happens to be -5. Use \pgfmathsetmacro to assign the result to a macro.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \pgfmathsetmacro\result{10*2}
  \node at (4,-5) {$2 \cdot 10 = \result$};
\end{tikzpicture}
\end{document}

To obtain an integer value, use \pgfmathtruncatemacro instead of \pgfmathsetmacro. For more information see the TikZ manual; in version 3.0.1a this topic is presented in section 89 on page 923.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \pgfmathtruncatemacro\result{10*2}
  \node at (4,-5) {$2 \cdot 10 = \result$};
\end{tikzpicture}
\end{document}

tikz performs some calculations when using \nodes. These calculations are done using \pgfmathparse. As such, your \pgfmathresult is overwritten with something else.

Instead, place the \pgfmathparse immediately before \pgfmathresult, or store \pgfmathresult immediately after evaluating it for use later:

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
  \pgfmathparse{10*2}\edef\storeresult{\pgfmathresult}%
  \node at (4,-5) {$2 \cdot 10 = \pgfmathprintnumber\storeresult$};
  \node at (4,-6) {$2 \cdot 10 = \pgfmathparse{10*2}\pgfmathprintnumber\pgfmathresult$};
\end{tikzpicture}

\end{document}