To solve the equation \( 4.72(x - 6.56) = 10.4 \), you would first divide both sides by \( 4.72 \):
\[ x - 6.56 = \frac{10.4}{4.72} \]
After calculating \( \frac{10.4}{4.72} \):
\[ \frac{10.4}{4.72} \approx 2.204 \]
Next, the equation becomes:
\[ x - 6.56 = 2.204 \]
To isolate \( x \), you need to add \( 6.56 \) to both sides of the equation.
Therefore, the number that should be added to both sides is:
\[ 6.56 \]