To solve the equation \( 4.72 ( x - 6.56 ) = 10.4 \), you would first divide both sides by \( 4.72 \):
\[ x - 6.56 = \frac{10.4}{4.72} \]
Now, let's calculate \( \frac{10.4}{4.72} \):
\[ \frac{10.4}{4.72} \approx 2.2067 \]
So, after dividing by \( 4.72 \), the equation becomes:
\[ x - 6.56 \approx 2.2067 \]
Next, to isolate \( x \), you need to add \( 6.56 \) to both sides of the equation:
\[ x \approx 2.2067 + 6.56 \]
Thus, the number that should be added to both sides after dividing is \( 6.56 \).