Mutliply the bold numbers
$1\times 9=9$
$\frac{\begin{matrix}\:\:&7&8&4&\bold{1}\\\times &\:\:&\:\:&\:\:&\bold{9}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&\:\:&9\end{matrix}}$
Mutliply the bold numbers
$4\times 9=36$
$\frac{\begin{matrix}\:\:&\:\:&3&\:\:&\:\:\\\:\:&7&8&\bold{4}&1\\\times &\:\:&\:\:&\:\:&\bold{9}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&6&9\end{matrix}}$
Add the carried number to the multiplication
$3+8\times 9=75$
$\frac{\begin{matrix}\:\:&7&\bold{3}&\:\:&\:\:\\\:\:&7&\bold{8}&4&1\\\times &\:\:&\:\:&\:\:&\bold{9}\end{matrix}}{\begin{matrix}\:\:&\:\:&5&6&9\end{matrix}}$
Add the carried number to the multiplication
$7+7\times 9=70$
$\frac{\begin{matrix}\:\:&7&\bold{7}&3&\:\:&\:\:\\\:\:&\:\:&\bold{7}&8&4&1\\\times &\:\:&\:\:&\:\:&\:\:&\bold{9}\end{matrix}}{\begin{matrix}\:\:&\:\:&0&5&6&9\end{matrix}}$
Add the carried digit,
$7$, to the result
$\frac{\begin{matrix}\:\:&7&7&3&\:\:&\:\:\\\:\:&\:\:&7&8&4&1\\\times &\:\:&\:\:&\:\:&\:\:&9\end{matrix}}{\begin{matrix}\:\:&7&0&5&6&9\end{matrix}}$
Line up the numbers
$\begin{matrix}\:\:&7&8&4&1\\\times &\:\:&\:\:&\:\:&9\end{matrix}$
$=70569$