To find the value that correctly fills in the blank in the expression \( 32 + 72 = __(4 + 9) \), we first calculate the left side:
\[ 32 + 72 = 104. \]
Next, we examine the right side of the equation, \( __(4 + 9) \). First, we can simplify \( 4 + 9 \):
\[ 4 + 9 = 13. \]
Now the equation becomes:
\[ 104 = __ \cdot 13. \]
To find the value of the blank, we divide both sides of the equation by 13:
\[ __ = \frac{104}{13}. \]
Now, we perform the division:
\[ \frac{104}{13} = 8. \]
Thus, the value that fills in the blank is
\[ \boxed{8}. \]