Modifying spacing inside align

I think you need to use the alignat environment, which gives you full control on the spacing between alignment columns. See it this code befits you:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{alignat*}{2}
    6 \times \left( 3+5 \right) &= 6 \times \left( 8 \right) &&= 48\\
    6 \times \left( 3+5 \right) &= 6 \times 3 + 6 \times 5 &= 18 + 30 &= 48
\end{alignat*}

\end{document} 

Two things:

1. align has a right-left alignment around & while you want some elements to be centred;

2. align inserts a large space between successive & to separate equations.

I'd suggest alignat with some box manipulations thanks to eqparbox:

\documentclass{article}

\usepackage{amsmath,eqparbox}

\begin{document}

\begin{alignat*}{2}
  2 \times (8 - 3) &=       \eqmakebox[c1]{$2 \times 5$}        &       & \eqmakebox[c2]{}         = 10, \\
  2 \times (8 - 3) &= \eqmakebox[c1]{$2 \times 8 - 2 \times 3$} & {}={} & \eqmakebox[c2]{$16 - 6$} = 10.
\end{alignat*}


\begin{alignat*}{2}
  6 \times ( 3 + 5 ) &=     \eqmakebox[c3]{$6 \times ( 8 )$}      &       & \eqmakebox[c4]{}           = 48, \\
  6 \times ( 3 + 5 ) &= \eqmakebox[c3]{$6 \times 3 + 6 \times 5$} & {}={} & \eqmakebox[c4]{$18 + 30$} = 48.
\end{alignat*}

\end{document}

\eqmakebox[<tag>][<align>]{<stuff>} aligns all <stuff> (set in text mode) with the same <tag> according to the specified <align>ment (default is centre, otherwise it can be left or right).

I propose a solution using matrix environment:

\documentclass{article}

\usepackage{amsmath}

\begin{document}
\[
    \begin{matrix}
        2\times(8-3)&=&2\times5&=&10,\\
        2\times(8-3)&=&2\times-2\times3&=&16-6&=&10.
    \end{matrix}
\]
\end{document}