To solve the equation \( 4.72(x - 6.56) = 10.4 \), we first divide both sides by \( 4.72 \):
\[ x - 6.56 = \frac{10.4}{4.72} \]
Next, we need to calculate \( \frac{10.4}{4.72} \):
\[ \frac{10.4}{4.72} \approx 2.207 \]
Now, we have:
\[ x - 6.56 \approx 2.207 \]
To isolate \( x \), we need to add \( 6.56 \) to both sides:
\[ x \approx 2.207 + 6.56 \]
Thus, the number that should be added to both sides is \( 6.56 \).