To solve the equation \( 797 \cdot 410 = w \cdot 797 \), we can use the properties of multiplication, specifically, we can divide both sides of the equation by \( 797 \), since \( 797 \neq 0 \).
So we have:
\[ \frac{797 \cdot 410}{797} = \frac{w \cdot 797}{797} \]
This simplifies to:
\[ 410 = w \]
Thus, the value of \( w \) that makes the multiplication sentence true is:
\[ \boxed{410} \]