Spivak calculus chapter 1 consequence of property 9 Spivak state's that one of the consequence of the distributive property is being able to solve multiplication of Arabic numerals.
    1 3
  x 2 4
  _______
   3 1 2

is arranged as: 
$13 . 24$
$=13 . (2 . 10 + 4)$
$= 13 . 2 . 10 + 13 . 4$
$= 26 . 10 + 52$
$= 312$
and
  1 3
  x 4
 _____
  5 2

is arranged as:
$=13 . 4$
$=(1 . 10 + 3) . 4$
$=1 . 10 . 4 + 3 . 4$
$=4 . 10 + 12$
$=4 . 10 + 1 . 10 + 2$
$=(4 + 1) . 10 + 2$
$=5 . 10 + 2$
$=52$
so why isn't $4 . 10 + 12$ directly written as $52$ like in the first problem?

He is showing us  how did he obtain $13.4=52$ in the first working using $P9$ property explicitly.

\begin{align}13\cdot 24 &= 13 \cdot (2\cdot 10 + 4) \\
&=13 \cdot 2 \cdot 10 + \color{blue}{13 \cdot 4} \\
&= 26 \cdot 10 + \color{blue}{52}
\end{align}
  The multiplication $13\cdot 4=52$ uses $P9$ also:

