The correct reason for why Shawnece would multiply both sides of the equation \( \frac{x}{7} - 4 = -6 \) by 7 is:
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
This step helps to isolate \( x \) on one side of the equation by eliminating the division, making it easier to solve for \( x \).